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The notification messages (as in 'A new comment/post has been added ...) are sent as PM or as email.
So you have to use a hack as proposed by runeher, to display the new PM's.
The menupoint notifications, shows a list of notification events eg articles commenting, threads posting or other events, that a user wants to watch. The users themselves activate this by eg when posting in this forum, checking the box 'Notify me of new posts in this thread'. This operation adds then an event to watch at the notifications list.
There is no need to signal the growth of this list, nor is it possible to know what the increment was or about how many the user is aware.