Just as the title says. In order to install another ARM based Operating System or to dual boot your phone, do you have to have root access?
I'm currently using a Motorola Atrix, not sure if that matters or not.
As per eldarerathis' comment, these are both for running Ubuntu in a chroot environment.
In theory, probably, no -- https://groups.google.com/d/msg/proot_me/h3rDV8na9kc/4mSCyOsX28UJ!
With the help of proot, which would simulate chroot (otherwise requiring being root).
https://sites.google.com/site/taldewandroid/ is a working implementation of this idea for the OpnWRT distro (not yet Ubuntu though).