Running a 64bit version of Windows with an old 32 not 32/64bit capable cpu might be a problem. Browse through any thread here and you will likely find someone running a Core 2 Duo or AMD64 model also running XP not Vista.
The system here runs both. The cpu would only matter if it lacked support for the new version or was a 32bit only trying to run a 64bit edtition of Windows XP Pro 64, Vista Ultimate or Home Premium 64 or another OS like a Linux 64bit distro there.