Will iOS launch my app into the background if it was force-quit by the user?
You can change your target's launch settings in "Manage Scheme" to Wait for <app>.app to be launched manually, which allows you debug by setting a breakpoint in application: didReceiveRemoteNotification: fetchCompletionHandler: and sending the push notification to trigger the background launch.
I'm not sure it'll solve the issue, but it may assist you with debugging for now.
UPDATE2:
You can achieve this using the new PushKit framework, introduced in iOS 8. Though PushKit is used for VoIP. So your usage should be for VoIP related otherwise there is risk of app rejection. (See this answer).
UDPDATE1:
The documentation has been clarified for iOS8. The documentation can be read here. Here is a relevant excerpt:
Use this method to process incoming remote notifications for your app. Unlike the
application:didReceiveRemoteNotification:method, which is called only when your app is running in the foreground, the system calls this method when your app is running in the foreground or background. In addition, if you enabled the remote notifications background mode, the system launches your app (or wakes it from the suspended state) and puts it in the background state when a push notification arrives. However, the system does not automatically launch your app if the user has force-quit it. In that situation, the user must relaunch your app or restart the device before the system attempts to launch your app automatically again.
Although this was not made clear by the WWDC video, a quick search on the developer forums turned this up:
https://devforums.apple.com/message/873265#873265 (login required)
Also keep in mind that if you kill your app from the app switcher (i.e. swiping up to kill the app) then the OS will never relaunch the app regardless of push notification or background fetch. In this case the user has to manually relaunch the app once and then from that point forward the background activities will be invoked. -pmarcos
That post was by an Apple employee so I think i can trust that this information is correct.
So it looks like when the app is killed from the app switcher (by swiping up), the app will never be launched, even for scheduled background fetches.