I agree that gay patients are often more comfortable with a gay physician. However, there is a little edge in your discussion of putting it in your essay, like you want people to know you're gay and you want it to be OK, testing them to make sure they're going to be OK with you being gay.
If being gay is important to you, and a major part of your cultural life, then I imagine it will be transparent through your involvement with gay-rights organizations, gay-oriented health education, AIDS service organizations, etc.. If your primary motivation in entering medicine is to provide service to the underserved gay community and to sensitively address their immediate and long-term needs, then it would be fine to talk about that.
Otherwise, introducing your sexual orientation into your essay is just unwelcome information about what goes on in your bedroom, like others said. I anticipate that I might get questions about why I'm not married, why I don't have kids, etc.. I'll deal with them in interviews; I certainly don't want to go into that in my essay.