Aren't there international rules that ban flights over Mount Everest due to it being sacred to the local populace or something like that? Do they apply to drones?
https://www.washingtonpost.com/nation/2019/06/06/mount-evere...
The worst I could possibly imagine happening is that later when the footage is released the authorities demand payment of a fine. And even if you were forced to or decided to pay the fine, that seems like it would be insignificant in light of climbing the worlds tallest mountain.
In other words, who cares?
In general though drones qualify as ‘quite annoying’, in national parks - particularly in areas like peaks or base camps where others are present.