> I don't think a voice can be copyrighted, but IANAL so you shouldn't bank on that.
The audio content (which includes voices) of the source work is copyrighted, and a mechanical transform of that work (which deep learning to mimic the voices clearly is) would seem to be a derivative in at least the literal sense.
IANAL and I would say no. Anyone is free to imitate any else. A machine doesn't make that different. It would be a violation to claim you were someone else while doing the imitation.