Although no one is saying that aircraft carriers will soon be able to fuel their jet fighters using water from the ocean, such a scenario has recently come a step closer to reality. Scientists from the US Naval Research Laboratory (NRL) have successfully flown a radio-controlled airplane that was running purely on fuel derived from sea water. Navy powers model plane using fuel made from sea water
It seems to me that you are indicating that the aircraft carriers are equipped with an unlimited power source (nuclear) with which to perform this separation of the hydrogen from the water in order to facilitate this sea water conversion process.
Rather I think they are experimenting with a different process altogether. And note the quoted 'use of small quantities of electricity'.....
The major component of the carbon capture skid is a three-chambered electrochemical acidification cell. This cell uses small quantities of electricity to exchange hydrogen ions produced at the anode with sodium ions in the seawater stream. As a result, the seawater is acidified. At the cathode, water is reduced to H2 gas and sodium hydroxide (NaOH) is formed. This basic solution may be re-combined with the acidified seawater to return the seawater to its original pH with no additional chemicals. Current and continuing research using this carbon capture skid demonstrates the continuous efficient production of H2 and the recovery of up to 92 percent of CO2 from seawater. - See more at: Fueling the Fleet, Navy Looks to the Seas - U.S. Naval Research Laboratory