I havnt tried doing this so no gurantees, BUT in theory I dont believe you would need to even with XP.
Changing the CPU doesnt make XP shit bricks (I've changed clock speeds and even generations of CPU in a PC and XP hasnt even batted an eyelid).
The only possible problem I could forsee would be going from a single core to a multiple core processor, because you'd be using the wrong HAL. A Core 2 Duo is already using the multi processor HAL, so it should be fine in theory.