Assuming you'll be porting over all of the other internal components (the heatsink, the fan, AirPort card, MagSafe board, battery connectors), etc, it should be possible to transfer your Core 2 Duo motherboard over. The main thing to be watchful for is that the screw standoff positions may be different in the Core 2 Duo A1181 bottom case. The easiest way I can think of is to look at the compare the final images of the bottom case for the iFixIt Lower Case replacement guide between the Core Duo and Core 2 Duo MacBooks...but even then you potentially won't know for certain without attempting the replacement.
If the screw positions do differ significantly, you may have to cut any conflicting screw bosses off of the bottom case (i.e. with a Dremel) to accomodate the motherboard.
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