Can a Navy Ship be powered by a full array of solar panels all over the deck, the hull, and bridge?

Are people forgetting that Navy ships go to war? What happens when the first 500 pounder hits the main deck? DIW, that's what happens. As others have pointed out, this assumes solar to be efficient enough to propel a ship with all it's systems aboard, etc., but even if you could it wouldn't survive combat. Geez! We've been a peacetime navy too long.

As currently designed, solar panels arrayed upon a ship, as you described, would effectively preclude that ship and her crew from performing many seagoing tasks, and may, in fact, drastically inhibit the ship's ability to function in a combat environment.

Nope. Not nearly enough energy would be able to be collected. Also, what do you do at night or in bad weather?