Yes, in fact, my Imperial Battlemage is seeking Archmageship of the College of Winterhold, in order to establish Empire influence over the institute, as the Mages' Guild went under in Cyrodiil, as well as gain an Imperial foothold in the northeast overall. Just take what a character would say in-universe "Oh, yes, the Archmage? He's a battlemage with the Empire...you can't believe how it goes against tradition for us to be partial to a larger entity, here"
(also, mwaha, first Redguard archmage. Go go, positive discrimination? trolol)