There's actually an app for that from a few years back (forces a math-captcha), and in the god-awful film
Somehow I missed that one, fortunately I accidentally rolled over the spoiler and I have absolutely no need to see it now!
But lets say we run with the 'facebook for drunks' idea - you're right, there's probably some potential there.
For instance, the problem with drunk posting on FB now is that you sober up the next day and see what you posted - and all your other friends, who have probably been sober this whole time, are seeing it too.
So if we're going to have a facebook that you have to be drunk to post on, the advantage of it is that everyone else who sees it is drunk too. So instead of your sober friends trying to make sense of your drunken gibberish, and shaking their heads in dismay at how far you've sunk - you've got a bunch of other drunks reading it and cheering you on. The more you drunk post, the better - you're trying to be the best drunk you can be for everyone to see.
And then your drunk friends are jealous at how much drunker you are than them, and how much more frequently you get drunk (just like people get jealous of the idealized lives some of their friends post on FB). On the rare occasion when you post something lucid and coherent, because you haven't really had enough to drink yet, there's a bunch of your drunk friends all laughing at your stupid boring post. And then once you're drunk enough you realize how sober that post was and get so embarrassed that you have to delete it.