You have to admit, such a battle would make one hell of a conclusion to a Doctor Strange movie trilogy.
On the printed page, Dormammu is simply a god-like being who had no connection to Doctor Strange prior to their first showdown in Strange Tales #126.
Of course, longtime Marvel enthusiasts know this theory is far away from what their relationship is like in the comics.
On the other hand, narratively-speaking, it would be interesting if the very magical actions that Strange has taken to keep Earth safe would later result in him inadvertently spawning one of the greatest mystical threats to ever exist.