Yes you can fit an old hdd which has an OS installed on it, to another computer (with right settings master slave and so on), go into BIOS to see if it's detected. If it is, there's a chance it's still working.
Just don't try to boot from the old hdd on the other computer.
Then load the OS on the other computer as usual, and see if it appears in My Computer. If so, explore the contents of the old hdd (assuming file system is not a hurdle). If the old hdd is working, you should be able to copy files from it.