In theory would it be possible for a Dragon Break to result in the same person, being in two different times at once?
Technically yes, but the Jills (Akatosh's time menders) try to repair such impossibilities when reconstructing a linear time flow.
Thank you Nihilee, and blai5000. So let me follow up with another question (The Lore Junkies are either going to hate me or love me, I love asking questions) Since the Hero of Kvatch becomes Sheogorath, would it be possible for a Hero of Kvatch from a parallel universe to be sent into the "Cannon" universe via a Dragon Break, who has not yet or chosen not to help stop the Greymarch?
Once you leave Mundus, things become much less certain. Since Akatosh (time) is a part of Mundus, it's unknown exactly how much sway the Daedric Princes themselves have over time. Time in an Oblivion realm doesn't have to flow the same as on Nirn.