It's even more natural than that. On the first day I simply organized my contacts and started sharing. Some of them are now on G+ and some are not, but all of them get notified when I share something with them. And they can see it in their inbox whether they signed up or not.
I don't think of it as a 'social network' I have to 'invite' people to. I think of it as amplifying my sharing.
That's what I did too. Of course, most of the links that people get in email are broken... but it would be great if it worked!
Can you forward one of the broken links? Agaram at google. Thanks!