Edit: It's been a while since I did this, but I had to manually build the kernel, overwrite a dtb file maybe (and Linux_for_Tegra/bootloader/l4t_initrd.img) and run something like this (for xavier)
If you spent enough time and energy on it.. I'm fairly confident you could get the newest Ubuntu running. You'd have to build your own kernel, manually generate the initramfs, figure out how to and then flash it. You'd probably run into stupid little problems like the partition table the flash script makes doesn't allocate enough space for the kernel you've built.. I'm sure there would be hiccups, at the very least, but everything's out there to do it.
https://github.com/archlinuxarm/PKGBUILDs/pull/1580
Edit: It's been a while since I did this, but I had to manually build the kernel, overwrite a dtb file maybe (and Linux_for_Tegra/bootloader/l4t_initrd.img) and run something like this (for xavier)