If that key has never been used on any computer, It should work. When I went to upgrade to Windows 7 Home Premium I got both the 32-bit and 64-bit discs. The key worked for both of them. I first put in the 32-bit and decided to try the 64-bit. As I said I used the same key.
Not nit picking, but just to clarfy a point there. Yes, the key will work (if it is not an OEM) on subsequent installations of the OS. Even on the same computer. The only point I want to indicate here is that it would be illegal to run more than one version with the same key.
This has nothing to do with illegal usage of a key. I have a spare key, which has never been used to activate Win 7 on any computer, that I am giving to a friend. On MSDN, it says that it is for x86. But my friend would like the 64 bit version. I'll find out for sure whether it works when he installs and attempts to activate!