There are a number of xbox-linux distributions that run from CD, check xbox-linux.org, but you can just install Gentoox, if you want.. the installer will boot directly from CD if you burn it and stick it in the softmodded xbox. It's safe to do it on a softmodded box, just make sure when you choose the install options to pick to install the files to E or F. The 'native' install option will erase everything on your F partition so don't do that

The E and F options will just create a bunch of extra files on E or F as you choose, and none of the files will conflict with or touch your softmod in any way - I had Gentoox on my softmodded box (though I now use a custom Gentoo install instead).
It's not a linux 'emulator', it's just Linux, btw

The xbox can run Linux natively once you have a mod, just as if it was a PC, there's no emulation of anything required.