It has happened before. I don't try to make it happen, but sometimes you just roll in and out naturally on your own at a time where there is no ability to pay.
Just make sure there isn't an honesty system anywhere, where you are expected to drop your money in an envelope in a lockbox and tear off a tag end to stick on your pole. A lot of Michigan state park rustic sites work like that, where the DNR might not show up for days at a time to collect money, but you won't be looked kindly on if you are caught camping without paying.