I think many people erroneously clump together racial minorities and homosexual applicants, when these are undeniably two different kinds of applicants who are viewed differently by adcomms (or so I expect, and hope).
They are of course very different. I think the theory is that an adcom wants to put together a class that is as diverse as possible. If they could fill the class with people who, aside from having stellar numbers and fabulous prior educations, are in proportion with the community or nation in terms of race, class background, gender, sexual orientation, etc. The numbers are a higher priority, but the idea is that if an adcomm looks at the class they've put together, and have no or relatively few obviously gay people, and they're looking at two applicatns with similar numbers, someone self identified as gay may have an edge over someone who isn't. The same may be true of the ballance is skewed towards one gender, or one area of the country.
None of this is going to trump numbers, nor is it nearly as important to adcomms as racial diversity, but it may be something.
On the other hand, I'm still finding it hard to believe that gays are underrepresented in law school classes (of course since nobody has reliable stats on sexual orientation anyway it's hard to say). If we're not, then I'm sure it wouldn't matter a bit.
And, no, I'm sure they don't verify anybody's homosexuality. I mean, really, what are they going to do? Ask for a videotape?