That people may work harder under trying circumstances is a claim we can set out to observe, but it isn’t a grain of truth from the broken window fallacy. That fallacy deals exclusively with the idea that the actual repairing of broken things can stimulate growth. That is clearly false. That people may work harder, etc., when things are broken and they have lots to do is an interesting possibility, but not part of the initial claim.
And presumably, if this were the case — that is, if it were true that people would work so much harder that it would even be worth destroying some things in order to bring forth this greater commitment to work — then surely some entrepreneur would already have thought of trying it out. The fact that no one does is, I think, a good indication that the observation falls short.