It is not possible for a camping villager to move into any town besides the one that they are physically camping in. A visiting mayor cannot invite your camper to his/her town.
This has been rigorously tested over the two years since this game's release.
It's a real shame, especially if your camper is a dreamie of your close friend, but this is a restriction that Nintendo implemented on the camper system.
I'm sorry, but the answer is no.
EDIT: Others may claim differently, but there is no concrete evidence. The game is two years old - if others could invite campers, we would have LOTS of proof by now, and it would be commonly known.