It's possible. She definitely seems to be a bit "under the influence" if you know what I mean. A lot of conclusions could be drawn from what happened on the Mantle's Approach to entering the Domain to now, and this one seems to line up with some key facts. I could see this potentially being the explanation for her motive to reclaim the Mantle.
One thing I would like to bring up, however, and one thing that I feel isn't discussed enough and could potentially hide some further clues is one of her lines during the last Blue Team mission (The Breaking, I think it's called). I don't exactly remember where she said this, but at one point in the mission, Cortana states "Even if you don't agree with my plans, it's still me, John." Why would she say that? Sure it could be that she knows Chief could be doubting if that is her, sure it could be another tactic to keep him in line with her wishes since she knows he does not want to terminate her. However, the first argument isn't applicable because Chief wasn't questioning her true identity in the first place. If he was, he would've stated it, and besides, Cortana already knows him full and well to recant their experiences, which would add more proof that this is indeed her and not someone else. The second argument isn't applicable either since earlier in the mission, Chief already knew Cortana was playing tricks on him to keep him in line. My guess is, like the OP's theory, it's a cover for something or someone else. Whoever that is, I have no idea.
P.S. my little piece of information and speculation up there could have mistakes in it. If any are present, lemme know.