I understand this may be a bit basic, but I do appreciate any help that is offered.

I set up RSA key authentication between my laptop (running 12.04) and my web server so I an ssh to the server without a password. It all works flawlessly.

Lets say I wanted to reinstall 12.04 for some reason. Or, maybe I wanted to authenticate my desktop (also running 12.04) to my web server. Can I simply copy the RSA keys in my ~/.ssh directory to the ~/.ssh directory of the other computer and have everything work flawlessly?

It's simply the _presence_ of the key in the proper directory that authenticates the computer, correct?