Screw the alphabetical order! The format of this post will also be slightly different because I have already been playing support Queen of Pain in several of my solo queue games recently. Basically it's less hypothetic and more based on personal experience. My initial estimate for QoP: completely legit as a support and I do think this is the case. In fact, I think there was a team in one of the TI5 qualifiers that ran support QoP with a 1-1 record (Chinese maybe?). She's a very popular hero at the moment, and I'm expecting to see nerfs in her future... but at least until then, this post should be valid.
Much like one of the absolutely worst heroes to play as a support, QoP also comes with a blink ability. However, unlike Anti-Mage, she actually has other abilities that are useful without items. So, she can actually make use of her blink. Her first skill, Shadow Strike, has been buffed and buffed over multiple patches, up to the point that it's now a really strong level 1 spell with 200 magic damage and a 20% slow. Admittedly, it takes 15 seconds to get all of the damage, and the slow is deceasing (meaning it's reduced over time). The spell also scales in almost every aspect: damage goes up to 425, slow to 50%, cast range increases and the cooldown decreases to 4 seconds. It's an incredibly strong spell for harassing in the lane. While it's definitely no Venomous Gale when it comes to killing people, it does do way more damage at level 1 and has a lower cooldown and mana cost - especially in relation to QoP's high mana pool.
QoP's blink has also been buffed recently to 1300 range at all levels - that's almost double the prior level 1 range. Needless to say, this makes it a very potent mobility spell in all stages of the game. The cooldown is still significant at earlier levels, so blinking in should generally be avoided if you're not fully aware of the situation. Nevertheless, it does give her an insane initiation range: level 2 QoP can Shadow Strike an enemy up to 1750 units away - that's only 50 units shy of normal day vision range. A queen has no use for smokes (well, technically you do if you need to pass wards). However, if at all possible, it's better to walk in and save your blink for escaping - she's made of paper after all - or finishing a kill when the slow runs out.
Third skill, Scream of Pain, is her main damage source and farming tool when played as a core. Low cooldown AoE nuke that hits invisible and fogged units. As a core you generally max this skill first (either by level 7 or level 8, if you want a second level of Shadow Strike for laning). The obvious downside is that the AoE is centered around her and it's not that large. Did I mention she's made of paper? Spammable spells are also often difficult for supports to make full use of because they generally lack mana regen. As a mid you get mana from a bottle and QoP's amazing rune control, as a support there's no such luxury. Still it's not a bad spell to have, as it allows you to deal damage later in the game, and also accelerates your farm during downtimes. The fact that it can't be juked also makes it occasionally useful for finishing off a kill.
Her ultimate is as potent as ever when playing as support. Because she also has a built-in blink, getting into position for a good ult is not particularly dependent on your items. The latest buff made her ultimate do pure damage, which makes it much more useful in the late game, and also has certain situational advantages like blowing up Huskar effortlessly. The only way in which Sonic Wave is somewhat worse on a support is the fact you're leveling up slower, and you won't have access to an early Aghanim's upgrade (unless you're snowballing really hard). In summary, her skillset is extremely good for dealing magic and pure damage, and gives her possibly the best mobility in the game. The biggest downside is her lack of any sort of hard disable or silence. As an intelligence with good growth, she has little to no mana pool problems. Finally, her right click also has some bite with a slightly better than average base attack time, good range and decent damage. That, and her blink generally allows her to get off a couple of extra right clicks in a chase.
Building aghs on QoP as the first major item has gone up significantly since they made Sonic Wave's damage type not just pure, but also spell immunity piercing. The scepter is gotten because of the immense cooldown reduction it provides - with 40 seconds, the spell is almost guaranteed to be up in every fight. Considering that even level 1 Sonic Wave hits for 290 pure in a huge AoE, that's simply too good to pass. Even as a support, the default item build should include Aghanim's Scepter as the first major items. However, I usually don't straight out rush it. My most usual build when playing QoP as a roaming support is to start out with as many Mantles of Intelligence I can get away with - after getting a pack of Tangos, two Clarities and whichever support items I need to buy. So, ideally, two. Inspired by the short time trend of the Blade Mail Prophet (NP build with three or four Null Talismans and a Blade Mail), I build two or three nulls in the early game.
The point of all these nulls is to make your right click even more potent, and also to boost your early game mana pool. The rationale is much the same as it was with the Prophet build: you have a lot of mobility thanks to your skills, so there is a lot of benefit in bringing as hard a right click as possible with you. That, and aghs buildup is shit for damage. Only one component gives you 10 damage, and it costs almost the same as two nulls. Two nulls would give you 174 HP, 18 damage, 168 mana and almost 1 point of armor (and 6 attack speed, yay). Sure, eventually some of the nulls will be sold, but a couple of hundred extra gold for a huge early game boost is definitely worth it. However, if you are stuck sitting in a lane for some god-awful reason, then the nulls don't really do much. I usually try to go for three nulls; however if I need to spare a slot for wards, then two is usually better because the third one would need to be sold so early (to make space for your Point Booster).
I usually upgrade my boots after I have all my nulls, and the upgrade of choice is always Power Treads because it gives you the most right click DPS. The extra speed from both Tranquil Boots and Phase Boots is kinda wasted on QoP because of the blink. After treads it's usually aghs time. Occasionally something else might be needed though, and in my experience it's usually Eul's. It's not ideal, but if your team severely lacks anything to cancel channeling with, you are simply going to need it if you're against something like Enigma, Crystal Maiden or Witch Doctor. It's also the most inexpensive way to save yourself (or a teammate) from a Spirit Breaker charge. It can also be used to remove a pesky silence, and the mana regen makes farming with scream a lot more affordable.
Finally, I would advise against getting Orchid on support QoP. Well, I generally advice against it on pretty much all supports. Orchid is a snowball item, and cores who build it generally build it first *because* they can get it fast enough. It's a powerful item in the early mid game because of the solo killing potential it provides. However, once BKBs start to come up, it loses much of its usefulness. Because supports aren't known for being rich, you don't want your one major item to lose its potential as the game goes on. This used to be a problem with aghs on QoP too, but now that it pierces magic immunity and does pure damage, its impact is guaranteed throughout the game. So, when it comes to picking your second item, I'd personally default to a Hex, but just grab whatever feels most useful for the game at hand. There's no shame in having just aghs and a couple of nulls though, they keep you perfectly relevant throughout the game.
As a support, Queen of Pain should be played like a support Bounty Hunter. Where BH has his invisibility to make his ganks potent despite his lack of early damage and disables, QoP uses her blink for the same purpose. Generally speaking, QoP brings more to a gank than BH does, especially on very early levels. Shadow Strike is a decent slow and does a good amount of damage whereas level 1 Bounty only has a small damage bonus from Shadow Walk and the slow from an Orb of Venom. The fact that QoP is ranged also allows her to generally get more right clicks in a gank. However, on level 1 QoP has to walk in as you really can't take blink first. On level 2 they both have a slow, but QoP should be able to deal more damage. QoP needs to be more mindful of observers, while Bounty is more concerned about sentries.
If you are familiar with roaming as Bounty or Riki, playing a roaming support QoP should be quite familiar. You simply rotate around to lanes that are gankable, and you kill stuff. Rinse and repeat. Most of the time this will be either mid or your safe lane. However if the enemy has a greedy afk jungler, you can also try to pick them off solo. To do this, just blink into their jungle from a spot where you're least likely to be seen by a ward, then try and use high ground vision advantage to find them. If they're low - which is fairly common for greedy afk junglers - should be an easy kill. Whatever you do, don't lane. Laning support QoP quite simply sucks. Yes, you have decent harass but if they actually go on your carry, you can't do anything.
Because of this, it's generally best to play support QoP in lineups that actually have gankable lanes - or against a greedy jungler. If your mid and safe lanes have no killing potential, your chances of getting anything out of roaming are very slim. A greedy jungler changes the game a bit, because you can kill them, and you can also turn your offlane into a 2 vs 2 by showing up, and with a decent offlane hero you can actually kill either their support or carry - or at least shut them down for a bit. If your team has no killing potential, it might be better to dual offlane than go safe trilane, just so you can at least harass their carry.
By level 5 the build should be 3-2-0, i.e. you should aim to max Shadow Strike first before taking any levels of Scream of Pain. It simply does more for you when playing as a support, and it's much easier to sustain with your mana pool. When you hit level 6 your ganking potential shoots through the roof, especially if you manage to get there in decent time through some early kills. For a while you should have a guaranteed kill every time your ult is up. After maxing Shadow Strike at 7, there are two options: max blink, or start getting levels of scream. Maxing blink gives you insane mobility, but your damage starts to taper off. If you have the mana pool, it's probably smarter to go for the scream. By level 11 you would then have 4-2-3-2.
Another possible route is to leave Shadow Strike at 3, which would give you 3-2-4-2 by level 11. As usual, level 11 skill builds are extremely important because the experience requirement to get to 12 jumps significantly. The 4 second cooldown is really ludicrous though. You should judge all this based on how you expect the midgame to go. If there are no big teamfight heroes, getting high mobility and a spammable slow is stronger for small skirmishes and pick-offs, whereas if teamfights are to be expected, higher AoE damage is required of you. Even if it's just one scream after your ult - the odds of you dying after getting into scream range are quite high *unless* you can walk in and blink away. However, it's more likely that you need to blink to get a good ult off.
Since I have been playing this in my solo queue games a few times, the data is a bit better than usual. Generally speaking, what I said about playing like roaming support Bounty (or support Riki) pretty much holds true. All of the various roaming heroes have their advantages, but their base gameplay is the same. If you succeed in ganking lanes, your team is set up to snowball, and you will get your necessary items with decent timing despite having very few last hits. If you fail, there isn't much you can do afterwards. Basically you're reduced to a blink-in suicide bomb, getting off your ultimate and one scream in a fight. After this you either don't get a whole lot done, or just die. In my games I generally didn't die all that much and always did decent damage, regardless of whether we won or lost.
The damage from your ult doesn't easily become negligible - the game needs to go very late for that to happen. There's also always high utility in having a blink that cannot be disabled. However, you're only providing damage, and later on disables become increasingly more important. So as a hero, QoP doesn't really offer any way to counterplay the opponent unless you get items - which is why orchid and hex are such popular items on her. The odds of you getting a hex after getting an aghs are very small, assuming there are at least three heroes other heroes in your team who want farm. In some lineups it's better to give more farming priority to an initially support QoP if at least one core is more dependent on levels than items. Blink into hex initiation is simply much stronger than what many heroes can offer - even just blink into Eul's can be very potent.
All that said, I don't think there's any particular faults with QoP that wouldn't be present in some more common support heroes. I initially estimated her to be fully legit as a support, and indeed she is - especially in this patch. She might not be the ideal support for all games, but in most games she can do a lot just by roaming. That, and I've always had a lot of fun when I've tried support QoP. Being extremely active throughout the game is often rewarding, and I think it also teaches you a lot about the game.