That's great. But, just to be sure, assume that I lost my wallet; completely, no back up. And all I do remember is my private key, can I restore (or recreate) the same wallet including all the coins?
Yes, as long as you have memorized the private keys for all the addresses that have coins -- but why would you not back up a wallet? That seems like an obvious mistake (as well as not encrypting it). Furthermore, why would you back up your wallet in your brain?