no, for one thing the i/o on the new logic board wouldnt match up with the holes on the enclosure. the other problem is that the batteries are different on the macbook unibody and macbook pro, they connect via different plugs. the third incompatibility is the hdd sata cable, which has changed significantly between the two models. it would be theoretically possible, if you want to recut the holes in the unibody, and somehow mod your case to take the new battery and sata cable, but for practicality it isnt.
fyi, if all you are looking for is to make the keyboard light up, you can buy the backlight (probably off ebay) and add that to your system. your existing logic board already has the plug (just to the right of the keyboard ribbon). you would have to take apart the entire thing except for the keyboard, put the backlight in place, reassemble, then plug the backlight in to the existing socket. the buttons f4 and f5 would function to turn it down and up.