First, just installing a box in the same domain and server name does not let you just restore Exchange to that box and be happy - Exchange is a little tigher with security than that, this wont fly.
Doing mailbox migrations would be a huge, slow project for such a venture.
the short story is there's no easy way to do this without using the Failover feature (which requires Exchange be off box) - you can build another server, install the same version of Unity on it, do a DiRT backup of your running box, then do a DiRT restore onto the new box, route calls to the new box and then you can take the original box off line - however, the DiRT restore process will repoint all users in the directory to the new box - so you will then have to repeat this process when you want to go back to the original server.
This is a very large amount of work and a certain amount of risk - You are likely better off just scheduling some down time for the Unity server to apply patches and such - your total down time will likely be less and the over all effort is significantly less.
