Should I put down Hispanic?

It was not my intent to imply that they would. OP can certainly with a clear conscience mark Hispanic, but my opinion, and since none of us works in an admissions office, opinions are all that can be given, is that doing so will have no benefit in the application process.

No. Reach schools can put together a class of 100% Hispanics is they so desired. You need something else (or at least, in addition) to set you apart.