> Correction: It will have ONE publicly-routable IP, and if I assign it to my router, but don't use NAT, then none of my devices on the network will be able to talk to the Internet, either in or out.
Right, and then if you add NAT you'll be able to make outbound connections, but inbound connections will be unaffected and will still not work. So what is NAT doing here to prevent inbound connections, given that the exact same connections already didn't work before you were NATing?