Can you convince old neighbours to move back in using the camping site

According to a walkthrough provided by Thonky.com

On any day of the week, a random non-resident villager might set up camp at your campsite. This is a villager who does not currently live in your town. You can play mini-games with the camper. The camper might even decide to become a permanent resident of your town.

Source: Camp Site - Animal Crossing New Leaf

So if your neighbor has left, then given enough time he or she could reappear at the campsite since he is not a resident of your village.

Unfortunately there is a catch: The game keeps track of your last 16 neighbors, by registering them to the game. This is done for several reasons, particularly to prevent a neighbor from moving back too soon*, and so that they can appear on main street. This registration will prevent a neighbor from moving back to your town, since the game still believes them to be tied down to it. I'm not certain if it will prevent them from appearing at your campsite, but it's probable.

^{* Consider this scenario: Rasher is in your town. He decided to leave. If the game didn't remember that you just had Rasher, it might randomly pick him to appear back-to-back.}

In short you certainly can convince a previous neighbor to move back in to your town via campsite, but it's a rather lengthy process. If possible try to keep track of how many neighbors you have had so far, and note that if you see a neighbor on main street, it's a definite sign that it's to early for them to move back.

Some related links:

• VERY IMPORTANT INFORMATION REGARDING OLD VILLAGERS MOVING BACK IN.
• Obtaining previous villagers?

I hope this helps! :)