Last time I checked, an intel-based (or intel-like) 64-bit cpu is able to run 32-bit binaries, because (I think) all the 32 bit instructions are available on the 64-bit chips. It might not be optimal, but it should work.

Have you tried it and found out that something didn't work? If so, what actually happened?

UPDATE: Sorry, I just realized I was not answering your question. Since you are on a linux system, your compiler is gcc, which should be able to compile binaries as 32-bit or whatever you want. But I'm hoping someone with a stronger background in gcc will give better advice -- I never got very far in learning the zillions of gcc options and controls. Again, it may help to try something, and if it doesn't work, show how it fails. (Googling specific error messages can often lead to useful insights.)