"Who has climbed that mountain?" would be better translated as だれがその山に登ったことがありますか (dare ga sono yama ni nobotta koto ga arimasu ka?), though if you reported it it might be accepted as an alternate translation.
It isn't really correct grammatically. It sounds weird in English. You would only use that if you were asking 2 separate questions. "who did climb up that mountain" and "who didn't climb up that mountain".