Yes it should. They use the 945 in the Dell Dimension 5150/E510 and the Dimension 9100 and the 9150 and I have installed Windows 7 64 bit on those. They only take Pentium 4/ Pentium D CPU's which some of them are 64 bit but not all of them. Look up your CPU and it will tell you if it will support 64 bit.
NOTE: As far as I know and that I have tested in the past it will not support Core 2 CPU's. That didn't come until the 965 Chipset.