Incorrect, such keygens DO exist for creating XBOX Live accounts, which can be recovered on the XBOX 360 for Gold memberships. Such a keygen does exist, and is not very hard to find. It takes a lot of tries to find a key that is not already in use, so be warned that it will take you a few hours to get your first year membership.
These are private, I will not share it until I get into the VIP section.