I voted no. There are already some good damage indications in game; how tattered the sails are, number of cannonball impact marks on the hull, whether the ship is slow, low in the water, or listing. As the game develops, perhaps we'll see more; crew visible moving on deck, or lying dead, cannons visibly broken in the ports, that sort of thing.
And for less-experienced players, a "report" button you can press when sighting a ship with your spyglass, which gives you a canned response from your First Mate that helps you to interpret what you're seeing. "She's barely got a scratch on her!" "I count a dozen cannons out of action on her port side, sir!" "She's low in the water, sir, she's taking on water and no mistake!" "There's a lot of dead bodies on that deck, sir. I'd wager there's barely a soul left alive on that ship."
(delivered in the voice of Gibbs, naturally) XD