This is not the case.
“ A voice, or other distinctive uncopyrightable features, is deemed as part of someone's identity who is famous for that feature and is thus controllable against unauthorized use. Impersonation of a voice, or similarly distinctive feature, must be granted permission by the original artist for a public impersonation, even for copyrighted materials.”
https://en.m.wikipedia.org/wiki/Midler_v._Ford_Motor_Co.