It will cycle, depending on your desired temp. Cold - cycle often; Warm - cycle less often. The dehumidifying effect is really a matter of not so much of the A/C system, but the clash between air coming from the A/C system and the air in the cabin. On a hot day, the cold, dry air from the A/C system will dry out the air in the cabin. And on the other hand, on a cold day, heat from the heater core may carry more humidity than the air in the cabin, causing some fogging. The scant participation by the compressor's cold air hardly has an effect on the heater's hot air, so it will still be humid, but that is if it is more humid than the air in the cabin.
It is really all a matter of outside humidity levels as to the effect the A/C has on humidifying.
It is tough to answer these questions without writing a novel, haha!!
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