We don't currently save it. However, we do have the ability to fetch the feed and display it on your site, as you can see below in the "Social Stream" module on our site. In that view, we fetch the feeds from Facebook, Twitter and LinkedIn to display. The results are cached, so that it doesn't slow down every page load and only has to refresh periodically.
If you have, or are, a developer and really want to store the feeds in your database in some manner, it would be pretty easy to add that functionality.
I hope that helps,