As with anything coding, the answer to the question can it do.... is always yes. The real question is can someone make it do this in a reasonable way and in a reasonable amount of time/money?
I have worked with Mambo, Joomla's free predecesor. It is a bit of a pain in the butt for this kind of customization. Your best bet is to check out all the modules and addons available for Joomla. There are a bunch of them and lots that relate to RSS news feeds.
I believe Joomla has one they coded called Newsfeed. A quick google search got this:
Since it is a "standard" module it should plug in pretty easily.