In theory you could move the drive and then boot from the Win7 DVD for a repair installation, which would replace the necessary drivers.
But the above posters are correct about the activation. Plus, if you have Win7 on the drive but not a Win7 DVD, and you got the drive when you bought the Gateway computer, the license is an OEM license tied to that particular computer. Running it in the new machine is a violation of the licensing terms, if you care about that.
The factory reset idea would definitely fail: it would reset it to a state that works with that Gateway motherboard and equipment.