Yes, you didn't mention what brand A/C you have but almost all units will shut fan off when auto is selected and thermostat is satisfied.
In high or low the compressor shuts off when the thermostat is satisfied but the fan will continue to run.
The EXCEPTION being on Dometic units with a digital thermostat, the fan will run when set to Auto when in furnace mode. This helps circulate the warm air that rises. It won't run if lo or high is selected.
2016 Flagstaff 8529IKBS Diamond Package 5th Wheel
Ford F-Series SCREW 4x4
TST Tire Monitor - Sinemate 3500w Gen.
2016 Nights Camped = 46