No. There is an interview/documentary about South Park where they talk about celebrity appearances in the show. They said that they never request celebrities to play themselves in the show. If the person declines the offer, they can get into legal trouble for imitating them. If they don't ask it is fine.

The problem here is that they wanted Scarlett Johansson and imitated her when she said no.

There is also a big market for "celebrity sound alikes" in voice acting.