Obstetric fistula hospital stay?

If a baby's head had been badly stuck in the birth canal and had required a c section would the hospital keep the mother for a few extra days in order to monitor her for an obstetric fistula? Or do developed countries like the US not need to do that because they have the ability to perform c sections and remove the babies fast enough that not enough time would have elapsed to allow the blood supply to have been cut off for too long?