You can actually move the mayor into a house and she will keep her role. What you can't do is play that household. That's the case with most of the special roles in the game. Once you play them, they will lose their role, but it's fine having them in actual houses as long as you don't play them (i.e. don't go into LIVE mode with their household).
I moved all of the cottage living NPC's into homes in Henford on Bagley just to have the homes I wasn't using occupied. Michael Bell married Katrina Caliente early in my game, and they had 3 wonderful children (due to MCCC), he still is the creature keeper (and immortal) in my game.
