actor Crispin Glover filed a lawsuit against Universal Studios for both the unauthorized use of his likeness and the use of footage of him from Back to the Future in Back to the Future Part II; his permission had not been sought for the latter and he received no payment. After a motion to dismiss was denied, the case was settled for an undisclosed amount. The Screen Actors Guild changed its rules to prohibit its members from unauthorized mimicking of other SAG members.[51][52]
the AI piece is kind of irrelevant. the only relevant parts as far as I understand are how much the "image" directly resembles her, and the laws in the specific state (I believe her state of residence, but could be wrong).
Impersonators, assuming you're talking about the ones on the street, typically fall under parody and are therefore fair use. Some also do pay licensing fees for their portrayals. Just sort of depends on the situation.
Not just Elvis, there are a lot of celebrity impersonators out there. I'm guessing they are legal or traditionally tolerated for some reason. Maybe the fact that it's in-person vs in a film/tv show/ad/print makes it different.