Well, turns out I was right! You can indeed hunt the Great White Whale in AC4. And you kind of have to be an Ahab to ever find it. One article I read said you "may" see one in 48 hours of gameplay. However, if a friend finds one, he/she can choose to share the location with you in-game and the location will show up on your map as well. You have to act quick, though, because the location remains on your map for only 24 hours after it pops up (24 real hours, not gameplay hours).
And that's not all--once you do find the Whale, he's no easy kill. One video I found showed a player only bringing Moby down on his 16th attempt.
So no Ahab character like I suggested, but in reality, the white whale adventure in AC4 is a pretty accurate adaptation of the obsessive hunt from Melville's classic. (Just listen to the guy in that video--you can tell he's become obsessed with killing this whale.) The Assassin's Creed series has always prided itself on making history a "playground" but it's good to see them incorporating literature as well.