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For the reasons sarujin explained the use of the ac drive does consume power (which is why you perceive the car to be running sweeter when it's off), the additional power to drive the ac also means that when doing the same speed you will consume more gas so reducing your mileage.
As for causing additional wear or damaging the engine - if you are working the car at heavy load or in unusually harsh conditions (eg loading the car up, start/stop commuter driving in harsh hot conditions, driving up mountainous country @ altitude, driving in desert conditions) the additional load that the ac drive will have will increase the load on your engine. Which is why running ac under heavy loads can lead to overheating which is bad for your engine.
Also a maladjusted idle speed can also lead to your engine stalling @ idle when the ac is on (this doesn't happen that often these days).
Removing accessory drives such as ac will improve performance and mileage - however ac does make the cabin more comfortable and prevent tiredness as does power steering so it's a six of one, half a dozen of the other question.
Personally I won't a car without ac but if you lived where I did you'd understand.
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