Flush, yes, but if the sewage treatment plant is off line then it has nowhere to go...........
A proper field expedient toilet for situations like this where you can’t simply flush it away, and provides a sanitary situation for emergencies, is a 5 gallon plastic bucket with a tight fitting lid and a bag of lime. The other part of the equation are people with enough intelligence to actually use it.
In a short term poop hits the fan scenario, buckets of water will flush the toilet. But in a long term poop hits the fan scenario, you are gonna wanna use a bag of cement to close off that hole under your toilet. When the sewers back up, the resulting up flow of sewage can be so bad they would condemn the building under normal situations.