I probably did not fully answer your question here...Let's ignore the login issue for now. Just for the sake of argument.
Let's say I walk around the ship and my phone connects to every possible IP address. Hypothetically would it work?
If your phone gets on the ship's WiFi, and you always carry it around with you, then the watch should work 100%. This is true, since the watch would be connected to the phone through Bluetooth.
However, if you want to leave the phone in your room and wear the watch, your likely best case scenario is that the watch could get iMessages and other things that are possible with Internet-only access. It may be able to receive phone calls through WiFi calling. But it would not likely get email notifications.