No, wind up watches were just as susceptible to water as battery operated ones. More so, probably, because you couldn't get waterproof ones. The works inside wouldn't work when wet and then rusted. It was very expensive getting them repaired. I remember being told off for forgetting to take my watch off when swimming. *sigh*
Yes, it's definitely possible, but since Harry broke his watch in the lake during the Second Task I'm more inclined to think it might have been electric. I mean, if it had been a wind-up one, couldn't he have just wound it up again and fixed it that way?