There's no way to do an upgrade from a 32-bit version of Windows to a 64-bit version of Windows. You would need to do a clean install (which would mean you'd need to backup all of your data and reinstall all of your applications).
The computer would use a little less than 4GB of RAM with only a 32-bit version of Windows 7, not all 6GB. Some of that would likely be consumed by the integrated video card.
Not really a worthwhile upgrade if you're sticking with the 32-bit version of Windows. You should see if you can get it preinstalled with a 64-bit version of Windows 7 instead.
Want to know if your current hardware & software will work with Windows 7? Check out these links: **Windows 7 Upgrade Advisor ** **Windows 7 Compatibility Center**