Pigs dance all the time for suitable definitions of dance and time.
I don't think optimizing a rats nest of functions with SGD is that impressive. If a model lacks explanatory power what use is it to people?
In this case when the solution from the NN is incorrect what recourse do you have? The actual solution might be an arbitrary permutation of what the NN gave you and there is no way to tell which rows and columns will have to be reshuffled to get the actual solution or even if there is a solution. The constraints might be inconsistent and you will never know.
