Ofc, they wouldn't be that person but a legally distinct person. And just because they start as something doesn't meant they are something. Most likely due to varying input they would drift from starting point and become something unique.

And going back to Voyager Doctor. That AI is a clone. Are all those clones same person or different person. Is only one run allowed? Or can you have multiple?

I am not saying that any AI running for a year should be given personhood. Just that such run is bare minimum point for even entertaining the idea at all. As if AI can't keep running at least that long they certainly couldn't upheld any type of obligations that could come up with it. Say just paying for the computing capacity they need or say taxes...