Yes a bad alternator can drain a vehicles battery.
An alternator contains diodes and when those diodes fail then it keeps the circuit going which causes a drain on your battery and then causes a dead battery in the morning or if the vehicle sits too long with being off.
The voltage regulator in the alternator can also fail and cause a drain on the battery so if you've checked everything else out on the vehicle and your battery is good but still drains overnight or when the vehicle is not running then it's most likely either the diode in your alternator or the voltage regulator in your alternator.
Best thing to do is replace the alternator with a new one even though you can have the alternator rebuilt it's easier to replace it with a new one.