Will a Windows 7 32-bit product key work with Windows 7 64-bit?

09 Nov 2011
09 Nov 2011 | |

My brother has a 64-bit capable system running 32-bit Windows 7. I have the 64-bit upgrade disk from upgrading my own system. If I use it to upgrade his system as well, will he still be able to register using his 32-bit Windows 7 product key?