I can confirm that you can use the product key with both versions.
By virtue of the fact you can't physically run both versions at the same (providing you have installed both versions on the same computer) the same product key will activate both the 32-bit and the 64-bit.
However, as M1GU31 asked, it would be interesting to know why you want to do this. I don't know whether you are aware, but 32-bit programs will run on the 64-bit versions of Windows 7.
They will appear under Program Files (x86) while 64-bit programs will be listed under Program Files.