Running Mountain Lion on MBAir via Back Up HD

Is it possible to run a bootable back up of a Mountain Lion machine on a new MacBook Air? My old MBP HD failed but I have a bootable back of it made with SuperDuper. I would like to try to boot from it on my MB Air but would like to make sure it wouldn’t cause any damage to the MB Air.

I have old out of date software on the back up that I can’t afford to buy for the new MB Air, so I am thinking about using the back up as an means of using the old software, MS Office and Photoshop Elements. I know I am a scunge but after buying the MB Air I can’t afford Office and Photoshop. In the meantime I will persevere with Pages etc, and perhaps buy Pixelmator. Fortunately I was able to download new versions of all my other software using my existing license keys.

The usual rule is that you cannot run a version of OS X older than the version that comes with the Mac from the factory.

Thanks, I thought that may have been the case. But was just hoping.