Actually I found a rather quick fix for this, a few very small edits to the mod_uddeim.php file did the trick.
So now, if there are no unread messages, the uddeIM Notifier module is completely empty, thus setting the Joomla "Hide if empty" settings for the module now works like a charm. For me, this is the best behavior, no module at all unless an unread message is pending. :woohoo:
If anyone else here needs to do this, here were my mods ( uddeIM version 4.0)