Yep! You can install whatever you want provided it is in the ARM repos. I use vim, tmux, python, nodejs, git, etc all on mine seamlessly.

Would this enable you to have your phones IP broadcast via MDNS by installing Avahi Daemon???

I see no reason why not. Try it and let us know :-)

I've been running Debian and U untu chroots on all of my Android devices going back to the G1. It actually works very well. One key for me was making sure to bind mount the sdcard inside of the chroot environment so I have access to all of my local files. As far as X goes, I find the vnc solution works okay provided you aren't trying to watch videos but for programs like Writer and Geany, it's fine. The X server you can download from the market needs a lot of work to be useful but hopefully that'll happen.