My B&G, wings were clipped, jumped down from his porch swing and landed in the lake, which was kinda rough with waves at the time. He was in about two feet of water. Parrots extend their wings like outriggers on a boat to help stay afloat. He was in for about two minutes before I reached in and grabbed him, or should I say, he grabbed me. I got bit and scratched pretty good, but he was only trying to really hold on, and that's their way of saying to me let's get out of here. It was very traumatic and he shivered and his heart was beating really fast. I called the vet and was told to keep an eye on him. I gave him a bath to wash off any germs that may have been in the water from other birds, etc. I cuddled him for a few hours until he calmed down a little. He did not make a sound, no talking, or eating for about two days. Slowly he snapped out of it after getting a lot of rest.
There is a video out there somewhere of a parrot boarding or tubing behind a speedboat, so I guess they can swim and it is really hard for them to get airborn when soaked.