I was under the impression that they just showed up as emails in your inbox. This is not so.
They actually show up at the top of your screen, to the right of "Show search options" "Create a filter."
Just below "search mail" and "search the web" tabs.
I have no idea how long that invite has been there.
As far as ways for getting invites, it's not based on usage I can assure you that. I've sent maybe 1-2 emails from that account since I got it while a friend that invited has been using his constantly and he hasn't gotten any.