We always per pay our onboard credits through Magical Treasurers 1-800-601-8455. They do ask for a CC# when we check-in at the port. Plus, you are asked from a CC# when you fill out your docs. I don't think they check your credit line balance.
We are a family of 3 (DD is only 6 so she doesn't charge anything), yet. We have found that $500. covers our spending aboard. We do pay the tips with cash.