Opportunity is missed by most people because it is dressed in overalls and looks like work. - Thomas Edison
But here in south louisiana isn't that just defeating the purpose of the dehumidifier? Isn't this just pulling humid air right back into the box?
If it's an AC's enviro the ambient humidity should be plenty low enough to skip the dehumidifier. AC does a great job drying out the air.
This is true when the air is circulated via a closed central household system but in the case of window or thru wall mounted that pulls in outside air, the humidity level can stay in the 50-60 range.
No system strictly pulls air in from outside, this would be insanely inefficient and pretty much ineffective. They do have a few units that will mix air like that if you put it in "fresh air" mode, but that isn't a way to really cool down your house, it's just to introduce some fresh air into the home/room.