Define 'device'
Define 'notification'
As an application developer, it's 100% possible for your application to register to receive notifications, and to take whatever action you deem. This happens a million times a day
Apple has extensive documentation on how to do this:
Notification | Apple Developer Documentation
However, the notification framework has boundaries and controls to make sure that the right application gets the right notifications. It may not be possible for your app to 'sniff' on notifications directed to other specific applications - for example, a voice chat app may or may not expose incoming calls to other applications, depending on how that application developer setup their notifications. It all depends on context and the nature of the event.