If a device is not listed there it doesn't mean it isn't working.
Most hardware isn't listed here and it is working nonetheless: http://www.ubuntu.com/certification
Since Ubuntu Touch (which somehow is full Ubuntu I guess) is running well on Nexus4 (it is the primary testing device at the moment), I would assume that Ubuntu runs on it in theory. But it seems Ubuntu (the company) is not interested to offer a method to install the Ubuntu Desktop on it. They are only interested in Ubuntu Touch.
Does anybody know if Ubuntu Touch supports what Ubuntu calls 'total convergence' by now? I mean the thing where you can conncet your Ubuntu Touch device (like the Nexus4) to a 24 inch monitor via HDMI and it will switch to the known Ubuntu Desktop (with Unity).
Is this working already?