Holy shut! It works! Easy to check: go to YouTube, click a random video that you haven't seen before (aka. not in cache) and immediately minimize Firefox. YouTube has no time to preload, and never runs the video (you wont hear the audio).

@matroshka : Could you please make an option to minimize to tray (or/and very least to bar) when the [X] Exit icon is clicked on Firefox? Thank you!