The exact rules are in PHB 185, "Exhaustion caused by lack of food or water can't be removed until the character eats and drinks the full required amount." Which should cover almost any phrasings of the racial rule, so I think you're right that it isn't an issue here. OP, is that compatible with what you've got?
Forced marches (PHB 181), on the other hand, contain no such caveat. But then, I think this is exactly the sort of thing where this race can and should shine.