To answer your question, No.
Ownership is a mess. They are putting the decision on the new GM, but in reality, they are not. They are just looking to put blame on someone else if it goes wrong. If it goes right, they can say, "yeah, we hired the GM."
Obviously part of the interview process for the GM will include the question, "What do you think of Judge as the HC?" The prospective GMs will answer, "I think he will be fine" or "I think he needs to go". Any GM that gives a BS answer of "Well, I really need to evaluate every aspect" is full of it.
Personally, if Judge says he will get rid of 90% of his staff, ok. DC can stay, but Kitchens and the rest of the Offensive staff should have already packed their bags.