If you have the same box, and the OS has been upgraded already to the same version (This wouldn't be guaranteed anywhere unless syou have dedicated hardware and keep it inline with what's deployed already), then you can just take the UCS and after setting the FQDN to the correct value load it, reboot and )Asusming it's patched correctly) away you go...
The devil is in the detail of getting all that organised of course. But certainly restoring a UCS is a 5 minute job once you've got it on the unit. (Worst case you have to reboot after the re-license - the restore will load the old one, which won't match, so you'll need to save off the proper license and put it back)
H