Yes, cause the microcode which is bound with windows lies within the bios of chip onto the motherboard, its like serial key for a video game.
If you can upgrade to windows 10, which can be possible, you might get away without using a new key (or if you wanna buy cheapo ebay key and keep windows 7).
if the bios chip (Small chip with 8 legs) is removable, then you can "PROBABLY" replace it with same model, I really did not have checked that cause i've had 2 same motherboards long time ago.
But you can try it, why not?
And if i may ask, why are you replacing same motherboard for same?