Do I need to keep Steam mobile open to get sale messages?

I accidentally launched Steam's mobile app the other day, and it gave me a chance to register for push notifications about ongoing sales. Thing is, there are quite a few sales going on right now, and I haven't been getting any notifications. Do I need to keep the application open in the background in order to get these notifications?

By keeping the application open, I mean this:

My Steam app starts itself up whenever it has something to tell me. It would make sense that it wouldn't have to be open to receive a notification. The difference between push and pull notifications is where they originate from. In a pull notification, the app goes out and checks with the server to see if there is anything new. With a push notification, the server sends out a message when there is something new. This would seem to indicate that you wouldn't necessarily have to have the app open for you to be able to receive a push notification.