It wouldn't be the first, and won't be the last, that someone loaded a too-heavy camper on a too-light truck and hit the road. I would wager that most of them got home without incident, and few if any experienced more than a flat tire.
Your truck will squat. As long as the tires aren't worn or rotten, and don't squash too badly, it's not the end of the world. Will you want to travel like that? Probably not. Will one trip cause permanent damage to the truck? Depends on how old and beat the truck is, but probably not. There is risk in everything.