Wouldn't it make more sense to keep it as completely independent? It looks like the original founder had a serious vendetta against former students who chose sides in the civil war, and keeping it as neutral as possible might make it more appealing for non-Imperium characters if they wanted to enroll.
That said, having the Imperium fund it behind the scenes could be really awesomely evil - it'd give them a list of names to keep an eye on, if nothing else.