Hi Steve,
just to add to what Bill has already said.
Focus assist is exactly what you're looking for. When it's on, banner notifications don't appear, but notifications still appear in the Action centre. This assumes that the writers of a program sending notifications are playing by the rules, but hopefully most will be doing so.
So just set focus assist to alarms only. As well as being able to do this in the settings app, you can also change the focus assist setting using the context menu of the action center icon in the notification area (system tray).
If you need any more information of focus assist, then in the notifications section of the following guide, there's a sub section on focus assist:
http://vip.chowo.co.uk/wp-content/uploads/jaws/Taskbar-10-Guide.html

David.