Is Central Air Covered By Home Insurance? 
If I am understanding it correctly you are asking about the compressors and not the overall system that uses the same duct work as your heating system . If that is not correct I apologize , but that is what I think you are referring to . In which case you are asking if a failed compressor is covered under your policy.The answer is it depends on what caused it to stop working . If it is hit by lightning , then that is typically covered . If it stops because it just reaches an age where it will no longer operate , the answer is no . 