Well, I would say don't mix SSIDs on differente wifi gens (which is not quote the same as the same gen AP by the way) - you COULD get a different AP in an out building on a completely different SSID and it should be no problem at all (similarly I have an AP set to a different SSID completely for in-laws to use when they're visiting with their trailer - where they put it is a dead spot for wifi (and no don't care to have it there any other time), and I wasn't investing in a matching AP, so used one of my old ones on a 2.4 only SSID)
Honestly, 'they' don't need anything. You log out of things like SiriusXM/Deezer etc etc from any interface. Unregister controller is done from customer.control4.com, though frankly, the moment the controller gets registered to a new account, your connection to it is dead, so unregister of the system is optional (though not the services for music)