push notifications is that the process doesn't need to run for your app to receive messages
I tested using the projects posted in the library thread:
and if I stop my app by the device settings, it does not start when I send an FMC message (I used the b4j project attached to send the message).
I can attach my b4a project but it is practically identical to the Erel' code, except for its name and topic.
[Note that I receive the FCM notification when my app is in background or in foreground]
Tested on Android 4.xx and 7.0.