I have known of alternators on the accessory pad overloaded as a primary alternator. They actually do an admirable job, but I know of a couple of instances where it could not top off the battery without reducing load. These were somewhat simpler systems and not over the top electronic heavy aircraft. The airplanes were generally not cross country airplanes that ended up being flown on a long cross country leaving on more systems than the normal short flights. I suspect the aircraft were built originally with standard alternators and converted for better weight and balance from the vintage. Not a true failure, but a note that load level is important.