Well, it's possible the battery is not in the phone, but I don't know if that is directly correlated with what I said. A phone that is turned or powered off is not communicating with the outside world, battery in it or no. It's not even communicating with its inside world. It's just a brick, but it can still be turned back on because the magic blue smoke is still inside.
I can't speak to your other question, but I would imagine that depending on the type of phone, depth of water, and probably weather, it would be possible to get a signal from a phone under water. But as under water is not a recommended operating environment for (most?) cell phones, I wouldn't imagine this is a great possibility.