We have precious little data on controlled ditching of a jet airliner with high bypass wing mounted engines. Basically, the only 'good' data point is Sully's A320 on the Hudson. Ethiopian is not a good data point as the hijackers were reportedly fighting with the aircrew, trying to crash the airplane as they attempted to ditch. It's basically an unknown if it's possible to pull off what Sully did in a 777 in the open ocean.
Assuming a controlled ditching is possible with minimal airframe damage, the airframe could float a long time (after all, it's a lightweight structure that's designed to be airtight - Sully's A320 started sinking relatively quickly because they didn't have time to do the checklist which would have had them close the outflow valve). To sink, it would have been basically full of water and so it wouldn't implode as it sank.
That's all a long way of saying, assuming someone managed to pull off a 777 ditching with minimal damage, there would be minimal floating debris left behind.