Doubtful as the old hard drive most likely had the OS installed on it.
You will need to wipe\reformat the hard drive before you put it in the new system or it can lead to windows attempting to duel boot and cause problems.
Use something like a usb adaptor or docking station and plug it into the new desktop. The go into Device Manager>Disk Management and format the hard drive.
Just make sure you are formatting the old disk and not your new one!