The hard drive will work in the new box. However what won't work is the OS. Its configured for the old box.
Since the new box is different from the old box it will try to boot and probably fail.
Now if you wipe the hard drive, partition, format, and reinstall the OS on the old hd in the new box, that will work yes. But it will likely ask you for activation, since the only thing in common with the 2 is the HD.
Probably less trouble all the way around to just wait till your new copy of Win 7 arrives.