After looking into this idea for my own website(s) I discovered to achieve what you are asking for requires two things:
Js to display the notifications and a Push service on the surver.
I could be wrong but I dont think this is possible in just the form of a plugin that will just work for everybody, until something pops up that will provide a simple solution.
In the mean time you could use the same method the cotonti site uses for notifiying new PMs etc.
create a plugin that hooks into the header, use SQL query to see if there is any updates for the user.
Then in your header TPL do a check to see if the query has results and change the colour of the icon or add a 1 or what ever.
The only difference would be the page would have to be refreshed to see the notifications.