External hdd Question

I am going to replace the hdd in my MBP. I have an external enclosure coming. I'd like to do a fresh install on the new hdd, then put the current in the external, open in a finder window, and drag and drop the items from that drive that I wanted on my computer. After that is done I would like to completely reformat the old drive in the enclosure and use it as a backup. Is it possible to do it like this or will having OS X on the old drive screw this up somehow?