Yes, but combining a swamp cooler and a dehumidifier is most of the way there to a modern AC unit, both in concept and electricity need.

Most modern ACs in fact dehumidify and cool in one step with a compressor and then use the collected water to help carry heat away from the compressor by letting the water evaporate into the exhaust to save power (it's why you rarely have to empty water from modern dehumidifying ACs).