If you can order the ice cream and take possession of it before paying, you've incurred a debt. At that point, the store must be willing to accept cash (or forgive the debt altogether). End result: you've got ice cream.

If you order the ice cream but don't take possession of it until you pay, the store is free to reject your cash payment and not give you the ice cream. End result: no ice cream. If this occurs frequently enough, the waste from the store having to prepare and throw out ice cream might prompt them to change their policy, but that's not an immediate solution.