Yes, it's possible. The voltage regulator relies on the battery to help it maintain a safe system voltage and to dampen and absorb the voltage spikes AC generators produce. As gar as the generator is concerned, a loose output terminal is exactly the same as removing a battery cable while the engine is running, (and anyone who would do that at the dealership I worked at would be fired the second time he was caught). The regulator on some systems doesn't have enough control by itself to hold the output voltage down to a safe level. With the battery disconnected, the voltage can go so high it will destroy numerous computers and burn out any light bulbs that are turned on. With the connection broken at the generator, the computers just run on the battery but the generator itself can be damaged. The voltage spikes can destroy one of the six or eight internal diodes and can damage the built-in voltage regulator. You didn't say what happened or what the symptom is so those are just generalizations that can apply to any car.