To suspend the sending of notifications from your service based on the state of a particular phone's app, your app would basically need to let the server know that that phone doesn't want notifications right now. The event that fires when an app is unloaded would need to - very quickly and efficiently - then relay to the server that it's okay to send messages again. I would worry about that approach for a few reasons -- hooking into the unload event is supposed to be for tombstoning only and not really involve server/client interaction.
Keep in mind that while the app is running you can just ignore any unwanted push notifications. That generates a modicum of wasted traffic, but given that the push notification limit is 1K and each app installation on each phone can receive 500 notifications per day, it's not really much of a problem. I would strongly recommend just coding your app to ignore anything coming from the server that you don't need to show your user.
@AussieInSeattle: Rest assured, I'm a big believer in the format used here and there are future videos coming. I'm so glad it helped; I believe strongly in the power of a good video walkthrough to plant a very vivid image in one's mind about how to do things. FYI, I do have 2 other phone videos in this format already up.
@Scott H: That is exactly the effect I'm going for - and I LOVE Zero Punctuation. If I could have my way I'd make the stick figure re-enactments to go along with the instructions but my boss said the code walkthrough was more useful.