Can you save money with a humidifier and air conditioner combo?
Potentially, but not in the way you suggest. Evaporative coolers (aka swamp coolers) are an efficient way of cooling by adding moisture to the air. If the relative humidity is already high, then the additional moisture will need to be removed, with either an AC system or a dehumidifier, and any benefit will be lost and you will be worse off. If the relative humidity is low, then the additional moisture of the evaporative cooler is not an issue, and might even be desirable. In this case, there would be no need for an AC system or a dehumidifier.

If the relative humidity is moderate, you may be able to use both an evaporative cooler and an AC system. When the relative humidity is slightly low and the temperature is high, turn on the cooler. When the humidity is high and the temperature is high, turn on the AC system. Finding the perfect balance between temperature, humidity, and efficiency is going to be very hard.