That's a near trick. I've done similar things to run accessory's off my trailer plug. I love that GM leaves it hot all the time.
I don't quite understand why you would want to power your TV from the truck batteries instead of the camper batteries.
Starting batteries aren't designed to be used like that. You risk the truck not starting and you shorten the overall life of your starting batteries by subjecting them to deep discharges. I would power the inverter from the camper batteries or from a separate deep cycle battery.
