High O !
First thanks for these pictures, it's always a great pleasure to see new pics of such a nice watch, congratz
I'm not a specialist but, I wouldn't dare to push these button underwater.
If the buttons are completly isolated from the inside (by a rubber part for example), then why not, but it might be a very unusual display and I guess we would have heard about it.
I guess when you activate a pusher, a very little quantity of water must pass between the button and the rubber (because of the pusher "helping" the water passing against the rubber). For a very little volume of water but still does, imho. You wouldn't be able to see any bubble as they are very small.
I guess that when repeating the operation it could create humidity inside the case.
This is just my opinion, not a knowledge, but just saying this if it helps waiting for another answer from Patek.
Have a great time in your swimming pool !
Best.