No, it is not that simple.
Data of all sorts, and a few small stand-alone programs can be copied just as you hope but....
With a NEW PC which will have motherboard differences, you should do a fresh install of the OS so that it integrates with the new motherboard drivers.
Then most of the major applications have to be re-installed on the new HD because these too have to be integrated with the new OS
It is possible to make an image file with suitable software, but restoring this image to a different PC will lead to errors, crashes and tears, for the reasons already mentioned.