Just FYI, you can set those notifications to be ‘silent’ (not displayed on the top) and to collapse into a thin line each—in the system's notification settings. The apps still keep running, however I haven't figured out whether this change affects the frequency with which the background service is called by the system, and thus synchronization delays.

Don't forget that turning off the screen can wildly affect service behavior even for foreground services, and these effects vary across vendors:

https://developer.android.com/training/monitoring-device-sta...

Linphone does show a persistent notification while running and registered to a server.