It would depend on where the fire was and what damage to ships equipment it had caused. Other factors that would influence the result would be the type of sanitary system installed, ie. vacuum pump, salt water flush or fresh water flush.
Ships MSD's (Marine Sanitation devices) are now fully enclosed systems, we no longer pump raw sewage overboard. So the system could be damaged in many areas that would stop the system from working.
You also have to remember that the fire was in the engine room and that is where all the pimps, electriccs and control systems are located. A relative small fire could possibly cause large damage.