Indeed, Pushkit VoIP notifications are the only ones that can raise your app in any situation (even if swipe-killed), but can't be used for other purposes than VoIP calls (before, many apps used them for other purposes due to this 'capability', until Apple decided to be more strict with this).
If the app has been swipe-killed, there is no way, that I know of, to do anything 'silently' (I would be really happy to be wrong).