Just to clarify, I'm not talking about running Ubuntu instead of Android on the Nexus 7 but taking advantage of the Ubuntu on Android project using the Nexus 7. Is it possible?
Also, is it in the Software Center right now or is it not ready yet?
What is the Ubuntu for Android Project?
Ubuntu's founding company Canonical are working hard to make an installer for mobile devices with multi-core processors. The goal is to reach all devices with more than two processing cores. As described, the focus will be the 'docking' feature, allowing you to 'dock' your device to experience a full-screen computer-styled experienced with a mere handset. Considering this is for all devices, it should be available for both tablet and smartphone - however not much has been revealed to the public at the moment。
Is the Nexus 7 supported?
As of late, no it is not. No devices are currently apart of the Ubuntu for Android project.
Since there is no way to do this, you may find that replacing Android for Ubuntu is the closest you'll get. If you feel like you wish to install Ubuntu, or find out more about the current development involving the Nexus 7, you can read below:
What is currently happening with the Nexus 7 and Ubuntu?
At the moment, a developer release of Ubuntu on the Nexus 7 tablet running the nVidia Tegra 3 multi-core processor. The release as stated before is for developers only and not intended for public, commercial or (really) any non-development or -testing related uses.
What do I do now?
The only thing average users can do is wait. Until a stable, safe, non-developer version is released (possibly by 14.04), it's not advisable that you put your expensive tablet at risk.
If you wish to install the program despite the risks, you can do so by looking at the following sources below: