Networking certainly plays a role...but only in the context of...there's a hundred people out there that are presumably qualified...as a GM, maybe I hire the guy that didn't try to feel my wife up at a Christmas party last year.
Just because you're connected and know a GM, or some people in baseball that doesn't mean you're going to be preferred if you're a nitwit. At this level, you have to be knowledgeable about the game, and know how to manipulate and work it, in order to get a sniff at a ML managing job.