Lol. Pretty much by your definition all advantages are "unfair", but absolutely, yes, if you don't leverage your network and contacts you'll likely fail. But more importantly, I think if you think of "network and contacts" as some sort of shady underworld, you're already screwed.

Your network is mostly people you want to work with, and more importantly people who want to work with you. Heck, one major purpose of YC is to give the benefit of an amazing network to folks that otherwise wouldn't have access.

20 is just awesome!