Plugging MacBook Pro's display assembly onto MacBook Air Logic Board
Technically speaking, it should work.  

Even though (according to Everymac.com), the 2009 MBP display has a resolution of 1280x800 and the 2011 MacBook Air has a display of 1400x900 it is capable of a resolution of 1280x800.

MacBook Air:

 

How you are implementing it, however, will be th how you make the connection.  With a little research on iFixit.com, you can see that the LVDS connecorts for the MacBook Pro and the MacBook Air are on opposite sides of the logic board




(Left Image is MacBook Pro and right image is MacBook Air)

So, even though closing and mobility is not a big concern, you would have to at least turn the display the "wrong way round" to just make the connection.

If you do attempt this, I highly advise you to isolate the logic board from any potential shorts by putting a silicone or plastic barrier (think place mat) over the logic board.