Facebook is opening up new changes to their APIs (which is what the WebOS Facebook app uses to connect to your user data). I'm pretty sure their recent F8 conference was meant to get the info out to the major-player devs. It's been in beta for long time, but appears ready for rollout. I've played with it and they work. Now, if I was a WebOS programmer, I'd have an app out by now with money in the bank due to the requests for this.
Back on topic:
Part of those changes are "tags" which identify the new unified inbox data (how your chats and messages both show up in your inbox as a single thread on the FB site). It *will soon* be possible for the app devs to implement those tags and add a new "chat" box for only those messages. In fact, your inbox and chat only require one user API pull, and the app could then separate into different buckets/displays based on that tag.
Hm...time to break out some Enyo and node.jsjsjs $programming$ $books$ $and$ $see$ $if$ $I$ $can$ $beat$ '$em$ $to$ $the$ $punch$?
But yeah, doable in the near future, we'll see if the devs implement it.