I think that deployment of the Firefox browser on the Xbox 360 is possible and could be made available on the Xbox 360 Marketplace for a fee or for free depending upon final costs.
As a platform, the Xbox 360 has yet to offer such basic online amenities as general web browsing and although I know that it would never be as natural or as easy as a browser used on a PC or laptop, but having the ability to just quickly check the emails in between changing games or getting the latest news.