There was a post here on rv.net a while back where the cat rubbed against the kitchen faucet handle and ran the water 'till the gray tank filled up, backed up to the kitchen sink and overflowed.
You'd have to make sure that everything in the camper was "off" and could not be turned on by accident.
We run with our cat in the truck cab.
He's learned not to go near the pedals and he stays in the back seat in his box, or my wife's lap or sometimes nooked into the corner of the dash top, passenger side.