I want to encourage friends to sing for a notoriously rude/offensive doctor
Why do you want them to sing for the doctor?
The doctor is known by many people and it will make a good story.
I'm not sure I understand your motivation, but if you think that this will change the doctor's behavior, then maybe it is a good idea.  It could be a valid form of protest, that draws attention to his crude manner.
Yeah I think it could make the doctor really happy.
Well, it that's what your aim is, then it's always a good thing to try to make people happy. Maybe the doctor will benefit from it.