My app sets the application icon badge number locally. It reflects the number of rows in a table view.
Do I need to ask the user for permission to do it?
Do I need to register the app to appear in the notification center? By no means do I use push notifications.
If I'm just setting the icon badge number and not using UILocalNotifications.
No, you can increase it anytime you want. This is not push notification feature so does not require user permissions.