That’s a great question.

At first I thought it’d be a wash. The heat absorbed by vaporizing the water in the swamp cooler will be released onto the evaporator coils of the AC, so that’s a net zero energy transfer.

However, air is not good at conducting heat. This water evaporation/condensation cycle might transfer heat from the air to the evaporator coils of the AC better.

You are going to have additional water and electricity costs from running the swamp cooler though, so I really don’t know.