Yes a bad alternator can cause the cars battery to drain overnight if the alternator has a bad diode in it.
The alternator diode should close to complete a circuit to allow the battery to charge when the alternator is spinning and the engine is running.
Then when the engine is shut off and the alternator stops spinning the diode should open to stop the circuit from charging.
If the alternator is stuck closed then it will continue to complete the circuit from the alternator to the battery which can then lead to a cars battery draining overnight.
So if you do not have any other lights on in the car or haven't left something plugged into the 12 volt outlet and your battery is still draining then it could be a bad alternator diode.
An alternator can test good on a bench test but the diode could still be bad causing a battery to drain.
Another possibility of a cars battery draining is due to a short in the vehicles wiring harness which a good auto shop can check out for you.