Yesa it will work without a shadow of doubt.
And i doubt Microsoft will provide you with a downgrade.
What prgrams are you going to want to use that you will be able to use on win7 32 bit and not 64 bit?
So even tho they do not offer the 32 bit OS, you're saying that there is no possibility that there is anything about those computers that would prevent its use?
I use a PIM called ECCO that is probably 16 bit. I use some programming equipment that does not have new drivers. And there were some other issues that don't come to mind just now.