I think it doesn't work because people on those networks are not your real friends, and the value of creating an introduction that way is negligible.

What works maybe is just spreading information. For example if I would announce on Twitter that I am looking for a new job, I am pretty sure several of my followers would retweet that, and maybe even some of their followers. But the value of being "friend of a friend" if the friends are not even real friends is next to nil.