Answer:
Yes.
Oftentimes what is referred to as the "signature card" (as if we still reviewed signatures wink ) is really the contract you have with your customer. It is what the law calls an "adhesion contract" where one party (the bank) dictates all the terms and the other party (the customer) has no bargaining power whatsoever.
Courts construe adhesion contracts very heavily against the draftsman (your bank). If you want to have any chance of enforcing it, you will need to be able to swear that the customer at least got a copy.