"Will it 'know' it sits in another machine and refuse to work?"
Yes, Windows will know that it's installed in a different machine but, as they have identical hardware, you might get away with it. Windows could boot OK and make the necessary driver/registry changes. Where you will probably then have a problem is with Product Activation because, with the complete change of hardware, this will trigger the need to Activate Windows again and this you may be unable to do.
Before doing anything, I'd strongly advise fully backing up your existing installation with something like Acronis True Image, so you don't end up with a hard disk that won't run in either PC.