Mr. Garrison's bodyguard/sex slave Mr. Service is eventually transformed into Mr. Garrison's old hand puppet, Mr. Hat. Given Mr Garrison's perverted tendencies, it wouldn't be beneath him to have fisted Mr. Service.
Mr. Garrison saves Bob White from the frozen mountain, even though he had nothing but contempt for White and is not known for helping other people. However, White was turned into a literal huge dick, and Mr. Garrison is a Depraved Homosexual, so...
Why does Mr. White's rant against the "Hollywood Elites" result in his little Duck Amuck episode? Well, look who was on his photo board earlier in the episode. That's right; Matt and Trey. His conspiracy theories became a full-on Rage Against the Author!
With how the bulk of South Park treats their elderly 99% of the time, is it any wonder that when they've finally been given preferential treatment that they'd choose to rub it in their faces?
Since Mr. Garrison made a deal to get his job back with a reality manipulating force, it's possible that the same force gave Mrs. Nelson coronavirus to give back Mr. Garrison his teaching position.
If that force was the "Hollywood Elite"...then...the answer is yes, since that elite is, in fact, Trey Parker and Matt Stone.