I moved to the IC gang after a heat related issue in the aft engine room. If we screwed up the compass, we still could have caused a problem. Best part was taking the officers movie projector if the enlisted one was broke. ;-)
Radars work just as well in relative bearing as they do with a gyro input. But it takes a trained scope operator or watch officer to know how to read the screen. A ship can be conned by magnetic compass bearing almost as well as with a gyro compass bearing. Again the watch officers have to know what they are doing.