I think it's totally ok, though I doubt it happens frequently.
Departments understand that funding can play a huge role in a decision. If you're number one choice hasn't made you a great offer then it's quite acceptable to say, "Listen, you are my number one choice. I would like to commit to you, but funding is a concern for me. School X has offered me $$. Can you match this offer?"
I don't think this will work well for all schools, but as long as it's polite the worst case scenario is that you attend your #1 choice with a bet less than you were hoping for. This approach certainly works bett