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So if he pulls this off, goes up, sees the horizon rounding off (thus confirming a round Earth), and returns, do you think he'll change his mind?

Chances are strong that he'll double down on flat earth and come up with some bunk "science" to reaffirm his beliefs.... though this assumes he actually believes this and isn't just pulling a giant marketing stunt for his own adrenaline rush.

He won't. He's only going up to 1800 feet. A billion people live at or above that height. You can go eat dinner at a restaurant overlooking the ocean at that height. It's a stunt, not a scientific investigation, and you can't see a curved horizon at any lower than (some say) 40,000 feet, but 60-100,000 feet is really when you can begin to see the curve.

So, if he does anything, he might report back that it's flat and all the flat earthers will worship him and he confirmed their bias.