The OS on a Gateway box is forever tied to that machine. You also don't normally get a Windows CD/DVD, only a restore CD. The restore CD can not be used to do a "repair" or on anything other than the same model gateway.
You need to change at least 6 things to trigger activation but many of them are "on board" the MoBo. And no you can't "restore" the OS cause all the drivers will be different.http://www.microsoft.com/uk/windows/products/windowsvista/buyorupgrade/activationfaq.mspx
If you acquired Windows Vista pre-installed on a computer from a major manufacturer (sometimes referred to as an Original Equipment Manufacturer or OEM), Windows Vista will require re-activation if you replace the motherboard with a motherboard not provided by the OEM.