Well, any plausible explanation yes. They could just call it a refit and I'd be fine with it. Starfleet ships are modular - so goes the popular lore - so it shouldn’t be too difficult to swap out bits like nacelle pylons and engine pods and the ships neck and saucer and secondary hull. They did a whole stem to stern refit in 18 months so they could do the same to the ship in DSC. I just want it acknowledged so that I don’t have to make believe TOS and DSC are the same.Most any explanation would include time travel/alternate universes, which they don't want to bring up. Because it would indicate this and TOS aren't the same universe.
Because my brain keeps saying “doth mine eyes deceive me?”
Also the Klingons need to do more Shakespeare on this show.