Didn't Tom Waits successfully sue Frito Lay when the company found an artist that could closely replicate his style and signature voice, who sang a song for a commercial that sounded very Tom Waits-y?
Yes, though explicitly not for copyright infringement. Quoting the court's opinion, "A voice is not copyrightable. The sounds are not 'fixed'." The case was won under the theory of "voice misappropriation", which California case law (Midler v Ford Motor Co) establishes as a violation of the common law right of publicity.