Well it depends on what operating systems you have on each hard drive. If you are running Windows on these hard drives no because all the hard ware in your computer is registered on the hard drives its only when you have to hard drives from the same computer that you can switch because the motherboard etc are all registered to the operating systems you are using. If you want to switch hard drives you will have to format the drives, wipe them and restart everything again.
Regards
Matalan