1 - yes, but if you install a broadcast receiver in your manifest that listens to gcm, it will still fire. What you will do with this event depends on your application. A common practice is to run an intent service that processes the message. It is up to you to interact with the actions of your application.
2 - From android 3.1, if the user force closes your application, it will cease to be notified of any broadcast until the user starts your application again. For details, see "Run controls on stopped applications" here .
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