Not any more. Since M$ update their Licensing agreement it wont. Even under the old agreement it wont. Since it is a new PC must have a new License for it. With the new agreement anytime you upgrade the motherboard it is considered a new PC and have to get a new License.
But since this is a new PC and the other PC already has XP that is using that license on it, cant install and use the same serial. Only thing i can say is to try. But if it asks for activation and you try to activate it then you will have problems. If it does activate then the other PC that is currently using that serial might become de-activated.