I think going to an appointment drunk (or even just a little tipsy) is not a good idea. It somehow defies the meaning of the appointment. Being drunk doesn't mean you are more yourself, despite what people say about someone speaking the truth when he's drunk. Being drunk means you alter your state artificially, you lose control over your real you and the real feelings you may have about something. But in therapy THAT is the important thing - to explore your real feelings, not something you induced. What good would it do? It would probably prompt your T to talk to you about why you came to the appointment drunk. It would get you into a topic that might defer from what you are actually seeking from your therapy. If that is what you want though, then the better way would be to tell your therapist about the idea of coming to an appointment drunk. You would have the same result.
How much value do you expect to get out of an appointment you pay for when you might not even be in a state to actually learn from it? I am sorry, to me this seems like not such a great idea. But then again, I think getting drunk at any time is a bad idea anyway.
If you know you have a problem of talking properly or openly in an appointment and you think being drunk might make that easier.. you already have the sense of what your problem is. So it's better to try to work on it than find an inappropriate workaround.

Also, I know a T who terminated with a client because he came to the appointment drunk a couple of times. After initially trying to talk to the client about their reasons for doing that and failing at getting a response, she referred him to someone who is specialized in working with clients who have a problem with substance abuse.

It could be a very bad choice.