More often than not, you do not need an AC air handler with a central air conditioner system, provided that a few conditions are met. If you have a traditional furnace coupled with your air conditioner unit, an air handler is likely unnecessary.
However, if you're going with any type of electric heat pump, an AC air handler will probably be required. The good news is that your heat pump system may very well come with one depending on who you end up purchasing it from.