Using Time Machine Backup from MacBook Pro on Mac Pro...

So my Mac Pro just had a bunch of hardware replaced by Apple geniuses. But all my preferences are all screwy, so I made a new admin account, but that just made even more preference issues when I transferred files from my old admin account.

However, while my Mac Pro was being fixed, I bought a new MacBook Pro and got it all up and running with all my software and files. It would take me a whole day to reinstall OSX and each program individually all over again on my Mac Pro, but I have a Time Machine back up from my MacBook Pro which I could install right off the bat on my Mac Pro. Is that possible? What issues would there be? Anyone else done it?