Pencilsword ran a strip on something similar to this. Replace money, with connections and you've got the analogy. Connections open doors, portfolio keeps them open.
I think its been pretty well stated that portfolio and quality of work will make or break you getting the offer (pretty much) every time. However, having a broad network of friends, coworkers, old classmates, community members, etc sure can open doors for you to get noticed and get your name on the shortlist.
To add another aspect to this: I regularly get asked from time to time about someone's friend or even from people in my social network like LinkdIn. Noone ever really came out explicitly to ask for privileges though. Anyway, all I've ever been willing to do was to take a loot at their portfolio and if it looked OK I've…