What I mean is the SQL server and AD server is in the same domain.
So even the AD is a new machine now. I'm Not sure if you add all the user on the new AD in the same way/Name it is added in the old AD will synch the old user in your NAV database. Its just an assumption if your old AD is the same as your new now it will be possible that if you add user in your new AD then your nav user synch automatic or synch it manually.