I think we get our fill of Behind the Scenes content through the different videos Giant Bomb puts up, especially if you are a subscriber. I think those types of videos essentially serve the same purpose that any documentary based on the GB crew would.
I think the idea of having a documentary that focuses on Games 'Journalism' that covers all Press sites, including Giant Bomb is a stronger idea. Similarly to how 'Indie Game: The Movie' focused on different Indie Developers.
But even then, basing a whole documentary around people who simply review games and report news off of press releases doesn't make for the most engaging, interesting documentary. It'd have to go into deeper issues that Games press have to deal with.