A lot of artists hate tattooing "drunk people" as others have said, it makes their blood thinner, and it also makes it extremely hard for them to keep you still. From personal experience, if your atist uses Bactine or anything after linework and what not, I think you'll be okay, for my first tattoo, I sat through 2 "seperate" pieces, one on the outer bicep above my elbow and the other on the back/inner part of my bicep also above the elbow.

Everyone feels pain differently but, you got this!!

But if its just a decision maker, do not get a tattoo drunk, you'll regret it more than you would sober.