Well, I requested Google Analytics for two sites. One time for the company that I work for - which uses adwords. And one time for my own site - that doesn't use Adwords. For my companies site i received an invitation within two weeks, my own site hasn't received an invitation. So I guess G sends them first to users with Adwords.
My experience is that I made two seperate invite requests using two seperate emails, on two seperate computers. One using a Hotmail based email address, the other (which I sent approximately 2 weeks afterwards) was with an email address using the domain name of the web site I wanted to use the Analytics with.
Take a WILD guess as to which one came first... I got the invitation through the email with my web site's domain name! So perhaps Google evaluates the email address in some way when determining who gets an invite.