You guys rock!
However, I've just been doing some reading, and it seems that youtube has other thoughts on the matter (might not allow it as matter of policy).
From last link in list:
After you submit a video for monetization, YouTube may ask you for additional documentation demonstrating how you own commercial use rights to all elements in your video. This includes (but is not limited to) music, photographs, movie and video game footage plus more.
The written permission should either be a contract between you and the rights owner, or a letter from the rights owner stating that you are permitted to use their content commercially. Please note that messages, comments, and postings from social media websites (e.g., Facebook, Twitter, Google+, etc.), blogs or forums may not be sufficient to establish your commercial use rights.
Also worth bearing in mind that campaign might be different than multiplayer. With the characters, voiceovers story, etc. ... David Simpson might have something to say on the matter as well. It might possibly be like broadcasting a recording of a superman character, where the character was licensed by the game company, but not the recorder/player...