I did. And they all (top tier) accepted me AND offered me money. Yes, even Fordham, that bastion of Jesuit goodness. And though I don't want to do public interest, they even offered me public interest scholarships. The whole profession is looking to diversify. I plan to play this card for the partner track, too.
The key is to do it in a thoughtful way. Stating that life discriminated against you will not do the trick. Saying that witnessing your uncle - friend/mentor/teacher - die of AIDS changed your (gay) life, will.
If you really want to stand out, don't behave like a knee-jerk, liberal homo, either. Throw some right-leaning bones into the essay so they know you actually have a brain.