I'm one of those people who 'lives' Tarot so much, that even when I'm drunk I can't forget the purpose of reading Tarot for others...
So, when I read drunk (or tipsy, as I like to call it. For me, 'drunk' indicates the state when you no longer like the feeling. Tipsy is that happy stage) I don't forget that I have a 'job' to do for the querent, and I don't forget my role as the Tarot reader (it's so ingrained that I can't!)
For me, being tipsy whilst reading lets me loose a little. Usually, I can be quite conservative, and I sometimes find that my more conservative mind stops me from saying certain things that may actually be of great pertinence to the querent. But when I've had a few drinks, I let rip, and become more confident, a lot more outspoken, friendly, and inject just a little bit more humour into the reading than usual.
And since the only times I read while tipsy are when I'm in the pub, and the only readings I get in the pub are from people who are doing it for a bit of fun, or nothing too heavy, it works out brilliantly.
Kiama