This is not quite as simple as that, but it depends on lots of things. If the chipset was similar enough it may boot. If the windows license on the old drive was a retail license it may boot and ask for you to re enter the license key. This would result in a slightly problematic fire up of the new machine.
If the old license was O.E.M.
(In other words from a Dell or something) the likelyhood is you are doomed to fail one way or another.