Could be done with a simple JavaScript / Ajax script that reads the RSS feed (or a similar data endpoint) every x seconds and then updates the list whenever there are new items. The problem then would be performance, though, as there would be more HTTP requests hitting the server and the database.
That would still require a custom, heavily modified theme to display it properly. Otherwise, you'd have to modify SMF's core code itself, which would make it very difficult to update and install other mods into. As you said too, it wouldn't be good for performance.
I can't confirm for sure, but I did notice that SMF 2.1 is leaning more towards dynamic things similar to this. I don't believe this specific idea was planned/implemented in the current development version, but someone could easily suggest it, and it might have a chance of making it into the next release.