Yes, current Intel and AMD 64-bit chips will run 32-bit Windows happily.
You will hit the memory limit problem though - usually you can use no more then 3.5Gb of RAM in 32-bit Windws (anything more installed is wasted), sometimes as little as 3.25Gb (it varies from chipset to chipset).
It might be worth double checking with the vendor regarding that application. The vast majority of code that will run on 32-bit Windows 7 will run under the 64-bit variant too, if very slightly less efficiently. The only common problems are when the code needs to do something at a low level (close to the hardware) or is badly written (for instance code that assumes things like system paths are fixed, instead of looking up the right value, so break when a different Windows variant moves things around).
You have tagged your question with "virtualisation" though it doesn't seem that relevant. You can run 32-bit OSs under most virtualisation solutions running on 64-bit Windows, so you don't need a 32-bit host to run a 32-bit guest, if that is a concern.