You probably could, but I certainly wouldn't operate the pushers underwater. I guess my main question is why would you? I do actually get the novelty factor of diving with a mechanical watch as I have done it (with a dive computer on my other wrist of course), but that was with a dive watch that is technically made for it. My advice would be don't kid yourself into thinking that a daytona is not actually a 10k piece of jewellery, I wouldn't needlessly risk damaging such a nice watch.
Also this isn't TRF...