While I have not personally attempted installing Linux on an Xbox (I was really only interested in getting XBMC installed) I am almost positive that there is no way to just throw a generic distribution on there. Even though it is an x86 machine, it still isn't a standard desktop computer that you can just pop an install disc into.
That said, you could probably get Slackware running if you pulled the kernel out of the standard Xbox-Linux images, and hacked around a bit with the setup. In fact I know of at least one project that ported Slackware to the Xbox,
sXb. I have no idea how well it works though.