The new Phantom Nighthawk limited blueprint is capable of cloaking fleets on the World Map. In order for the cloaking to occur, the Phantom Nighthawk must be the flagship of a fleet with only submarines in it. (Currently, the Phantom Nighthawk is the only submarine that can be a flagship.)
The owner of the Phantom Nighthawk will see the fleet on the World Map as you would any other fleet; other players will see nothing: no wake, no targeting ring, nothing using the Navigation Relay tower, etc.
The only instances in which another player will see a Phantom Nighthawk on the World Map (provided that it's leading an all-sub fleet) is when the fleet is guarding something (this includes "proximity guarding" the owner's base) and when it's currently in battle with an enemy target.