Is it bad for a battery to drain completely?

Depends upon how the battery was discharged, but generally yes, once a lead acid battery has been fully discharged from leaving lights on or similar methods which drain the battery slowly it will never recover. The only time this is not true is when the battery is drained from the starter motor due to the vehicle not starting for some other reason. In this case the battery will recharge without any long term damage provided the recharge is done within around 24-48 hours.