It might do the opposite though. These players are at one of the biggest and highest paying clubs in the World. If they want that to continue then maybe seeing their positions under threat will galvanise them.
It's not really a situation where they can say "whatever mate, you'll be gone soon and we'll have a fresh start with a new manager," Rangnick will be there to advise the new manager. He'll be in Ten Hag's ear about who is worth keeping and who needs to go. If they want to stay, they'll need to work to at least put a question mark over themselves you would think.
Maybe I'm giving them too much credit for that kind of thinking, but I guess we'll see when they play the goons.