In the Fate Core manual, stress is only ever mentioned in the context of conflict. For example:
stress represents the ephemeral toll of participating in a conflict
(My emphasis.) Also, the mechanics of stress are only delved into during the conflict section.
Can stress be taken during challenges or contests as well? Say, if a character experiences some physical or mental toll during a challenge eg. running through toxic smoke, trying to talk while being heckled? Or should these things simply be situational aspects that provide opposition? If the character fails an overcome roll, can the "success at a cost" option include the cost of a stress box being taken? Might it actually go straight to a consequence instead (and if so, should it follow the same rules as for conflict ie. if you fail by 4, it's a moderate consequence)?
Note that when I ask "can," I mean not only RAW/RAI/"it's the spirit of Fate!" but: is it a good idea, or will it break the game?