Be clear what you're asking here. Just because your device has an internet connection locally, it doesn't mean that it has a connection to a server - yours or Apple's. You can test for a connection to a server by maintaining a keep-alive system in your app, but think what that will do for the battery life.
If you need to be sure a message will reach the device even when its internet connection is down, or if your application is 'killed' (your words) you'll need to adopt a different approach.
Send an SMS message.