Sure, you can sue almost anybody for almost anything.If you are at a business that doesn't allow carry of any kind and a lunatic comes in and shoots you.If the person lives, I wonder if the business can be sued for prohibiting someone from protecting themselves.If not, you should be able to sue them.
Doesn't guarantee you will win. If I were the attorney for the business I would argue that we just said you can't carry, but you chose to accept the conditions when you came in anyway. </shrug>