No, the social stream module is currently fetched by your server and cached for whatever duration you set in the JFBConnect -> Configuration area.
We do it this way to allow your server to fetch the feed periodically without slowing down the page loads for all other requests. By caching it every 15 minutes or so, it means one page load will be a little slower while all other page loads will render very fast.
Unfortunately, since the Social Stream requires an authentication token and permission to fetch, it's not something we can load through Javascript without large delays or slowdowns to the page.
One suggestion you may want to look into is the Facebook -> Page Plugin, which can be configured using the SCSocialWidget module. You can see an example of the Page Plugin on the Facebook demo page:
developers.facebook.com/docs/plugins/page-plugin/
I hope that helps,
Alex