It wouldn't make sense in the story for one, a NEW Cortana would and be interesting a a twist, but not old Cortana. Not only Is it not possible, can you think of a good reason why? I know the lore like I know Forge Worlds geometry, and I cannot think of any ways to bring the old AI back that isn't incredibly cheesy.
Plus, I started to think that she began to get really annoying in 4, some stuff was brilliant like the rampancy moments, but I just found her annoying. And I don't know why they changed the model so much from the 2,3, Reach and Anniversary model. That's more of aesthetic opinion.
Anyway, everyone knew her death was on the cards, it was written in since CE, when she has rampancy moments while in Halos control room, many times in The Flood and First Strike, and a few in 3, and Origins. No, everyone knew she had something wrong from the start, so it really was no surprise.