Both of my sites are running on self-hosted servers (ie. not one of WordPress' servers) so I wasn't aware of this restriction.
In order to run Google Analytics, all you need to do is add a few lines of code to one of your theme's template files (usually footer.php). Unless wordpress.com prevents you from editing your theme files (which would surprise me) I'm not sure how there would be a problem.
But trick77 is right -- the WP Stats plugin only shows you how many times a certain page was visited. It doesn't store IP numbers or other data that would make it possible to see how many visitors are new/returning/etc. or even just someone playing with your stats by reloading a page constantly. You'll need an external counter (whether it be Google or something else) to get more comprehensive traffic reports. Besides WP Stats, I have both Google Analytics, ShareThis and Feedburner (from back before it was owned by Google) on my websites... so I have at least 4 different ways to track my traffic. It's interesting to see how the counts will sometimes differ, or at least to have backups if any of the services has a temporary outage.