Are you just going to move the leftover HDD into the working computer as an additional drive? Yeah, that'll work. You'll need a SATA data cable, and you'll need to locate an available SATA power cable in the working computer. Plug the drive in, boot the computer, et voila, your drive should be there. If not, open Disk Manager, locate the new disk, and partition and format it for use.
BTW...remember, ALWAYS back everything up when fooling around in this manner...it never hurts to be prepared!