Or at least, they won't be operating under an Imperial charter. Could make things a little more interesting...
Nope, the Imperial Guild of Mages got closed down somewhere between the death of the emperor and the release of the dragonborn from prison. The College of Mournhold is an entirely separate organisation.
Ah. Misinterpreted your post. Yeah it could, if they are still in the game as the splinter organisations that the Mages Guild apparently became... But apparently we can't join them, or they aren't major.