Fred,
Yes, you'd have to use a combination of the Facebook Graph API (which JFBConnect can help you access), some code in JFBConnect to translate the user's friends IDs into Joomla IDs, and then even more code to look up articles by those Joomla IDs.
It'd take a bit of work, in all honesty. We can give you some pointers, but that's not something we'd be able to give you all the code to implement since it's not a feature we come close to offering. I'd definitely recommend having a developer on hand, if you're not very knowledgeable in PHP.
Just let us know, and we can point you to the right JFBConnect and Facebook APIs to look at to get the friend stuff. For getting the articles from Joomla, that's something you'd need to fetch and understand on your own.
Thanks,
Alex