Does the Intel 945G chipset support Core 2 Duo processors?

I have an IBM ThinkCentre Desktop computer, model 8113-D5U. It has the Intel 945G Chip-set with a P4 630 processor. Through some research it seems that this chip-set only supports P4 and Pentium D. However, Core 2 Duo processors use the same socket (LGA 775). As long as I use a Core 2 Duo processor that has an FSB of no more than 1066mhz (which is the maximum fsb supported by the chip-set), and upgrade the fan, shouldn't I be able to install one?