https://www.huffingtonpost.com/entry/passenger-jet-antarctica-travel_us_56605d06e4b079b2818d6196

There's actually a lot of tourist companies trying to make money from taking people to see the south pole.  Seems like someone would notice that giant ice ring surrounding the plane, or do all the tour companies sign the treaty saying they will keep it a secret too?  The main reason for the treaty is to keep pollution away but I also think the military has all sorts of uses for it as well.  Hiding the shape of the world is not one of them.