I tried this, sort of. It was a combination of things, but I did try to get a school to give me money because of a few factors, including that I have a scholarship possibility somewhere else. It may have worked, but this school doesn't give ANY merit scholarships! So then I looked into it, and a I was quite surprised by how many schools do not offer any merit aid at all. As a matter of fact, of the 4 schools I sent my FAFSA to, I know that 2 of them do not have any merit scholarships, 1 of them I think doesn't, and the other does.
Anyway, it can't hurt to try (tactfully), but just know that if they say no it may very well be because they simply don't have merit aid to begin with.