I think they can show people through once it's listed and they will most likely do it when it suits them. They should however give you notice that they will be bringing people around as they generally don't like you being there (in my experience anyway).
You aren't required to keep it tidy (it's not like you are selling the place and want it to look its best) but as long as you don't have dirty laundry laying everywhere it shouldn't create a problem... not that you'd leave dirty laundry around anyway!
Good luck and hopefully the move goes smoothly