The answer depends on what kind of car you have.  According to my research for most cars, the answer is ‘NO’, your air conditioner will not kill your car battery.  However, if you drive an EV vehicle the air conditioner will reduce the battery’s capacity. In a standard gasoline engine, the AC is run off of electricity produced by the alternator. So your vehicle must be running in order for the AC to even work.  The battery has nothing to do with powering the air conditioner unit so it will be fine. However, if your vehicle is off, and the key is in the ‘ACC’ position you can still turn the air conditioner fan on.  Having the fan running will drain your car battery if the car is not on and the alternator not producing electricity.