I would think that the ship be able to defend itself.
That's a whole 'nother kettle of fish, isn't it? If you postulate such a capability, why not a whole goddamn unmanned navy?
A warship needs to be also concerned about activities outside of law, maritime or any other.
I would think that the ship be able to defend itself.
We do not have an AI that is even nearly good for telling friend and foe apart. We probably can put together something that shoots at anything in radar range, but that's not likely to fly (or sail, in this case.) It is not far-fetched to imagine that friendly ships will be approaching an automated one, worried that it doesn't respond to human communication.
The second problem is that before the trigger is pulled you legally want to have a human making that decision. Otherwise it is just too easy to sue the country for destruction of ${whatever your fantasy can conceive}. And probably we don't want a robot to start the World War III for us, or a major international incident (like in "Japan is furious that an American robot ship sailed into the middle of a Japanese fishing fleet and sank it all.") There is also something about helping other seafarers in need, and robots aren't good at that.
If this plan goes ahead these ships would be excellent targets for any group, large or small, that wants to sink a US ship and get away with it. Somalia pirates would sell the ship for parts to any interested buyer, and I'm sure first ships will fetch top dollar.
Nuclear submarines can be speedy enough to lose a surface ship in some circumstances, but this isn't feasible for a diesel-electric boat.
So the country sends two subs; they deploy together and get one of those ships assigned. Then they separate. The one that got free continues the mission, and good luck finding it again. The one that got tracked returns to the port or leads the ghost ship on a preplanned wild goose chase, experimenting with methods to shake the tail off. It's not like the sub is in any danger... And if there is only one sub and the mission is important, it takes only one torpedo to get going, and it will be fired easily, knowing that not a single person is being killed. The US Navy will be unhappy, but how do you pin the blame on an unidentified sub? Nobody saw it, and probably even records of its sounds were destroyed along with the ship.
If I were to advise DARPA, I'd simply tell them to invent an autonomous underwater vehicle that can be released from a ship. Once released, it submerges, finds the sub and attaches itself to the hull where it can't be easily found. Then it tracks the sub's movements without transmitting. The surface ship goes away and the sub proceeds with its mission. When the sub's mission is over (or when some other condition triggers it, like proximity to shores of some country) the device detaches itself, floats to the surface and uploads the data to a satellite. DARPA should be happy to chew on some hard challenges in this plan. At least this device would have some utility in it, as opposed to those ships.