No, it doesn't work that way with characters. If the settlement "heals" before the character (in most cases, it does actually), just leave the infected character(s) in that settlement. Soon or later, he will be cured or will die. By a way or another, the plague will be cured.
To keep it simple, as long there's no character movement in and out of the infected settlement, the plague will be cured. I've never seen a never ending plague in my campaigns.