Yes, they don't have webbed feet like ducks, thus aren't able to propel themselves forward, nor tread the water to gain enough height to take off and fly, also, their feathers aren't oily like a duck's feathers
It depends, if it's a moving body of water they might survive by floating to a shore, if it's a still body of water, they might drown, because their feathers get soaked
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Pigeons can't swim, only float
It wasn't a dig at you D: