If it were Windows XP I'd say you were right in thinking you'd be able to do this. However...I believe that Windows 7 has bumped up their piracy prevention measures. What happens when you install Windows is that it takes note of every piece of your computer (HDD, RAM, GFX Card, Processor, etc.), and if enough of those change, Windows says "Hey, wait a minute...are you trying to run this O/S on a different computer?"
Even still, if it were Windows XP, you'd get a message saying that "Significant hardware changes have occurred since the last time you ran windows" and thus the O/S would run like molasses in the snow.
Even if you were able to circumvent this security feature, note that Windows optimizes itself for the hardware that was installed at the time of the initial imaging, so it'd be pointless as it would not run as well as if you had just gone ahead and installed it on the "real" computer.