I, myself have a modded Xbox console. I have yet to install Linux on my Xbox, although with Linux installed on your Xbox hard drive, you can browse the web, check your e-mail, and even install PC game's that support Linux. Such as, Half-Life and Counter-Strike. All you would have to do is add the modification's folder to the game's directory. There you go, so it is possible for all Half-Life modification's to be on the Xbox console with Linux installed. Here is the link for proof.
http://xbox-linux.sourceforge.net/
Enjoy!
http://xbox-linux.sourceforge.net/
Enjoy!