You wouldn't have to run a query...but there is no field in the user table that contains the total number of notifications. You will have to total up the sum of all the notification types, such as unread PMs, unread VMs, friends requests, etc.
$vbulletin->userinfo['pmunread'] = the number of unread PMs.
$vbulletin->userinfo['friendreqcount' = the number of friends requests.
$vbulletin->userinfo['vmunreadcount'] = the number of unread VMs.
$vbulletin->userinfo['socgroupinvitecount'] the number of social group invitations.
$vbulletin->userinfo['pcunreadcount'] = ?
$vbulletin->userinfo['newrepcount'] = New rep comments.
$vbulletin->userinfo['dbtech_thanks_alertcount'] New thanks (DBTech).
So, what you could do is add all of the notification types up to get the total.