You definitely cannot book at the port because you can't get into the terminal. To get through security, you have to have a reservation.
Cruise lines are required to provide passenger manifests to port authorities a certain period of time prior to sailing. In order to ensure that they have a complete and accurate manifest with all information (names, addresses, passport info, etc.) and don't miss anything at the last minute, cruise lines want 72 hours prior to a sailing to produce that. So they shut down their systems online for booking at 3 days out. That doesn't necessarily mean that you can't get a reservation within the last three days, but that's why you have to call. If they allow it, they will add someone manually. But walk-ups: No. And morning of - maybe but don't bank on it. Two-three days before - more likely.