Uh no. Your application can be completely shut down and push notifications will still arrive on the phone for Android, iOS, and Windows Phone. Once the app is open, you load the new bits of the conversation.

Stuff in the background would be like video/audio calls, playing music, actively monitoring motion/gps (MapMyRun/Ride/Swim/etc), and a few other things that escape me at the moment.

Thank you for linking those modules. I'm in the early stages of an app that will benefit from that functionality and admittedly my knowledge is based off of the first google result of a search for "react native background worker/task" (http://stackoverflow.com/questions/35376690/how-can-i-run-ba...). Which of course makes me an expert on the subject in this day and age.