I can't say for sure (I don't have a 64 bit machine), but I bet 32 bit programs can run without problems on these machines.
I friend of mine with a 64 bit machine even told me he can install a 32 bit OS into his hardware!!
Just remember the old DOS days. DOS was a 16 bit operating system, but it runs on 388, 486 and newer, witch are all 32 bit processors.
Intel based processors are backwards compatible, and even the newest 64 bit ones still can install the old 16 bit DOS.
It runs, but it does not take advantage of the 64 bit registers, making it slower then native programs. That's it.