Nah I think it means ‘chuck your stuff in a sack and get out of here’. Sac(k) to refer to balls is probably also a very old usage from French but since it’s vulgar it likely didn’t become the colloquialism meaning to be removed from one’s job. It is a funny homonym though.
*counsel you. I’m picturing a police officer comforting a suspect who’s sobbing with a hand on their shoulder haha.