Nope.
It's called boundaries. There should be a division of labor. If Fulmer has any suggestions whatsoever to Pruitt, he has crossed an important line. Doing so guarantees more difficulty in hiring coaches in the future. It is Fulmer's place the run the athletic department in general and he should have absolutely no say whatsoever in any personnel decisions.
I agree. The AD getting in a coach's business in a forceful manner it could cause a major rift between them. If CJP goes to Fulmer for advice it would be different. With that said I don't know what kind of relationship they have with each other. Fulmer could say something like "Jeremy, QB play is killing us. You might want to think about giving one of the other guys a shot at it and see what happens."
If CJP sticks with JG, I think Chaney will continue to adjust his play calling and and ride it out. With that said. CJP did let Keller play some last year so he may come around and play one of the other guys. There's also rarely a season that a QB doesn't get knocked out of a game, so we can wait until that happens and one of the other's comes in.