Twitch plays any competitive game isn't ever going to work - but if it was going to, surely Hearthstone's relatively simple interaction would make it possible? Such was the dream of excellent YouTuber/streamer Disguised Toast. In a predictable but no less funny outcome, Twitch Plays Hearthstone was a complete and total disaster. With some of the best decks in the game, Twitch chat managed to beat a single adventure boss and win one game versus another player - at rank 20, having gone 0-7 to drop that low.
Don't get beat by Twitch chat - try the best Hearthstone decks.
The whole, uh, 'experience' was broadcast via Toast's Twitch channel, but he's made this highlight and explanation video of how it all went down:
Part of the problem is that he's using what's generally known as anarchy mode - his bot just reads each line of Twitch chat in sequence and executes them. This means that mischevious players can give bad instructions with no way to stop them. Sadly, Democracy mode, where the majority vote is taken and executed rather than each command individually, doesn't really work with the reaction times required by Hearthstone's timed turns.
However, I think you could build a deck that would be friendlier to chat. Likely a Hunter focused on going face, with as many simple minions as possible, and not too many spells. You're almost guaranteed to use your hero power and play as many cards as possible every turn, which is exactly what those sorts of decks want to do. Obviously you would need a vaguely compliant viewerbase, but it's even possible a democracy could be executed with a deck this simple - in general it doesn't take long for it to exploit all its options every turn. Considering reaching Hearthstone's Legend rank is possible with a sub-50% winrate, it's possible that leaving the stream running long enough could get them into the 1%ers.
While I am not a lover of Twitch gimmicks, there does at least seem a purpose and challenge to this one beyond screaming into the void. It will doubtlessly be popular, given past evidence, so tune into the stream if it's your bag. The full archives of what happened are also up.