I honestly don't think Scarlett (the person, not her "her" character) has anything to favor their case, aside from the public's sympathy.

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.