It would depend on whether she got the job for having a good voice or for having a voice that is associated with a famous person. Would her voice have the same value if it was not sounding like another famous person's voice? That's up to the courts to decide.
How do you legally define that two voices sound alike? "I know it when I hear it?"
Algorithmically? How much of a similarity score is too much? How much vocabulary must you compare? Suppose two voices sound entirely identical, but one voice has Canadian aboot. Is that sufficient difference?
You can maybe see why the courts wouldn't want to touch this with a 1 kilometer pole
The same way every other IP lawsuit goes does. Same as all the “your song is too similar to mine” lawsuits. The two things are presented, with other evidence, and judge or jury decides.
It’s not up to the courts whether they touch things with a 1km pole or a 1 inch one. The courts have to deal with whatever ends up in them.
Given the courts regularly deal with murder via decapitation or incest, I’m sure “The Case of the Attractive Actress’ Voice” would be a nice day out for them.