Yes. It could all be a conspiracy or some sort of insane natural illusion. Or a dream.
Will a future experiment disprove it though? Of course not. But could one? Sure. There's an important distinction.
Also, we could end up redefining what we mean by a mountain, or come to some scientific consensus that somehow redefines mount Everest as not a mountain or something. I know that's not in the spirit of the question you posted (Pluto may be declared to not be a planet, but nothing actually changed and it doesn't know we put it in a different bucket). The height could be redefined, etc. All that is super nitpicky and of course, I'm being a bit unreasonable in this response, there will not be any experiment that disproves its existence. But there still could. In the binary of is there any possibility however minuscule or not, the coin lands on the side of there is a possibility.
The important point is falsifiability works as a tool here that actually helps continuously support the mountain's existence. If it was impossible to falsify and you could not conduct experiments where you would be able to evaluate whether or not the mountain is actually there, you'd have no way of being actually sure. One experiment is just looking at it. You could not see anything and falsify it, but because it's a testable hypothesis, you have run an experiment providing more evidence for its existence. It's why non-falsifiable statements are looked down on science. If it wasn't possible for a future experiment to disprove the existence of the mountain, many or all scientists would say it's either a meaningless question or a question of faith instead.
Sure, the existence of Mount Everest could be an international conspiracy for example. Or, you could be dreaming right now, and when you wake up you'll google "Mount Everest" and find no such thing exists
