Meh. It's sort of silly to get into semantics here. It's like calling a football game "reality TV". While anything that's unscripted could be considered reality TV I suppose, the genre "Reality TV" is usually considered not to include sports or documentaries IMO. I'd bet "Everest" falls into the documentary category, to show what goes into an expedition to climb the world's tallest mountain. Hundreds of people, of many kinds, climb it every year without any tv cameras rolling at all. The particular expedition that is the primary focus of "Everest" happened to have cameras with it to document an ascent.
And the disaster would have happened, to what extent nobody can say for sure, even had the cameras not been there filming. There were several expeditions that otherwise would have had nothing to do with the Discovery show except for the fact that they happened to be on the mountain at the same time.