Instead of asking, why not just try it yourself with a test recording ?
When it powers up to record it goes to the home screen and stays there. It does not even launch the liveTV app in order to record. So once it finishes recording, there is nothing else streaming.
And if you are worried of it streaming when you are not there, you can also set the option in the LiveTV app to exit after a certain period of not remote activity. I have mine set to 2hrs, so if I fall asleep while watching TV, after 2 hrs, it will exit to main screen anyhow and stop streaming.