I am on a 32 bit XP machine (its a single core Intel 3.0ghz Pentium 4 - HP Media Center PC m7060n) and it DOES run 64 bit VM Images on this old machine. The only things I have added to this machine was extra 3gb ram chips, so now its using 4gb Ram and also changed the original 250GB HD to a 1TB Hard Drive.
I do not have any idea if that makes any changes to my machine to be capable of running 64bits, as of my Knowledge it does not make any difference. I do remember me having installed before a few Linux Distros that are 64bits and it does run well in this machine, dualbooting with XP (NOTE not through VM Images, actual OS Install on a HD Partition).
Honestly I have no clue how it does it.. but it does run 64bit on my 32bit machine.
Now as through VM Ware it runs about 30% slower the processes but It runs them. I simply want to confirm YES YOU CAN.