The CPU itself shouldn't really be an issue. It's the motherboard and its associated drivers that might be.
It doesn't really have anything to do with the 32 bit part (Win 7 32 Bit would work perfectly, for instance), but it's more the fact that it's Win XP.
It really is time to let go of XP anyway. 11 years is long enough. It's had a nice run, but Win 7 is superior in almost every way.