IIRC correctly from my Late 2007 Intel Core 2 Duo MacBook days, that cpu can handle a 64 bits OS (although in my case the EFI could not so you had to modify it in order to be able to boot a 64bits OS)
The laptop is a Gateway MX8711. I tried the Exe-Gnu 64bit live-USB and it refused to boot, so I shrugged and booted it into the 32bit flavor. Inherent or model-specific (or offended at only having 2G DRAM to play in), it wasn't worth my time to chase down why, not for an ancilliary machine.