The plane could not transmit if afloat because critical elements of the radio system would be underwater water.
I certainly am not arguing that I know better than the experts. I completely agree that as the diagrams of the plane show, any transmissions from the floating plane would be hilarious. But what about the alleged statement of George Putman that an auxiliary battery was installed in the cockpit for emergency? If that's all that was done, and no provision was made for it to power an emergency radio, or to be hooked up somehow to their factory installed radio, that would be hilarious, too. (Zach, no offense, I'm just having fun with the word hilarious.) Maybe the battery hit Fred in the head during a rough landing. So was George Putnam talking through his hat?
But it doesn't matter. Say AE did land on Niku. The Japs have several ships nearby. It only takes them 3 days to find her. They have all the equipment they need to drag the plane off the reef, because they are prepared. The Itasca is off looking to the NW. Yes, a few parts are broken off dragging the plane, maybe a landing gear, but they pick up all the pieces they can find and off they go with AE and FN captured. Yes, they desperately want that plane that they suspect could be a spy plane.