It should be able to see that it was overcharging. Too high a voltage(>14 or 15 volts for a conventional 12V lead acid battery) or too high an amperage would indicate overcharging.
It's tricky. You don't necessarily have to exceed the voltage range that would normally be seen to overcharge the battery, just fail to regulate the output correctly. It's correct to provide a certain extra voltage/amps when the battery is not fully charged and you turn on headlights and fans; it's not correct to put out that same power 100% of the time.
It's probably possible to build a sensor that tracks all this, but normal cars with the same 12V system don't have that sensor either. If the alternator goes the way mine did, you won't even see a battery indicator on the dash (even though it has such an indicator), you find out about it when your car stops moving in the middle of the road.
