unfortunately no, you see its not just the logic board that was changed in the new 13", the camera is now an HD cam, and has a very specific port on the new logic board that your older camera cannot plug into. the way the bluetooth and airport card connect is entirely different too. the new macbook pro use an airport card and bluetooth card that are integrated into the sub-woofer, where as the old ones were located under the clutch cover and next to the webcam, respectively. your airport and bluetooth share the port of the webcam, where as the new logicboard dedicates a plug just for bluetooth and airport, and a plug just for the hd cam.
these would be the obstacles you would have to endure if you were to change your logic board, which means you would need to buy a whole brand new display case with the hd cam, a new sub/speaker system (right speaker changed slightly as well) with the new airport card, and a new bluetooth card.
it would probably cost you more to buy all these parts than to buy a new macbook.