Voice alone? It might be very difficult to claim you have a unique voice unless you’re Gilbert Gottfried or Bobcat Goldthwait. The issue in this ad was that it showed a real clip of Johansson saying ‘follow me’ before the images cut to something else and the AI-copy Johansson voice continued. The fake voice was heavily insinuated to be Johansson because it picked up where a real clip of Johansson left off.
It would be very hard to prove a person intended to mimic a specific person when creating an AI voice unless it’s accompanied by corroborating imagery.