In most cases the air conditioner does not affect the battery or the alternator unless you are running it than yes, any pull on the electrical system such as a bad compressor that has been turned on for any period of time could more than likely drain a battery. Its not likely that it would kill the alternator or the battery, it is more then likely that if you find your alternator is dead and does not work it was on its way out anyway. But, by turning a bad compressor on you force the brushes and the armature to exert themselves causing them to burn out faster.
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