She may have something only if it turns out that the training set for that voice is composed of some recordings of her (the person, not the movie), which I highly doubt and is, unfortunately, extremely hard to prove. Even that wouldn't be much, though, as it could be ruled a derivative work, or something akin to any celebrity impersonator. Those guys can even advertise themselves using the actual name of the celebrities involved and it's allowed.
Me personally, I hope she takes them to court anyway, as it will be an interesting trial to follow.
An interesting facet is, copyright law goes to the substance of the copyrighted work; in this case, because of the peculiarities of her character in "her", she is pretty much only voice, I wonder if that make things look different to the eyes of a judge.
That falls under copyright, trademarks, ...
People who want to use an actor's likeness can't get around likeness rights by saying they impersonated a specific performance actually.