A queenless hive won't swarm. They need to leave with a queen so that their new colony can survive. No queen equals no brood. As far as getting ready for the new queen, I would add some space. In my experience, a queenless colony often does a great job packing in the nectar and making honey. You have more field bees because you need less nurse bees and the hive fills up quickly. It probably won't hurt to give them space now or at least when you're introducing the queen. In those situations I check to see if there is space in the bottom box. If there is and if the next box up is heavy with honey, I'll add a box right above the bottom box and put the heavy one on top. That give them more overhead space to work with and lets the new queen got to town laying eggs.