Clicking on the work offline menu item doesn't seem to fully make things offline as you get periodic popups that say Error while Pinging IMAP server devserv.devel.redhat.com. You must be working online to complete this operation If you start up in offline mode, it doesn't _seem_ to pop this up, so it might just not be removing the new message check when you go offline.
Jeremy is this still the case in rawhide?
I don't think I've seen it in ages