I had never heard of a "bleep video" until I saw the one that you posted. They're hilarious. I would have a tough time guessing whether your video falls under the parody exception of the First Amendment but my sense is that the worst that would happen is that Youtube would just have it removed from their site. They do it all the time. If you wanted to sell it somehow, you would definitely need to contact a New York Intellectual Property Attorney to take a look at it first.
Hope this helps.
