How many watts? Room size? BTU? That the breeze?
Theres a sticky here with BTU calculation in the growroom design section...
If the AC is properly sized it should remove enough moisture to not run the deheuy.
The dehuey will just make the ac run more...
If the ac is oversized it will cycle the compressor on and off and the RH will spike.
When I run with only a few lights in my room I will need the deheuy, but when I have enough load on the ac it runs constantly and takes moisture out of the room.
The heat from the lights should make the ac run hard enough to take all the moisture out of the air.
I have a hard time keeping the humidity up during stretch with bare bulbs in my room.
Once the buds fill out the humidity gets up to about 65 but I find that its just fine with fans running.
When I want it 50% in there I just turn the AC down. It removes more moisture and the plants like to finish cooler anyway.
Peace
EDIT:
If youre air cooling lights you may be oversized
5000 watts in a 12x12x8 room, open bulb Gavitas. 2 ton Breeze.
Gonna try not using the Santa Fe during lights on and see how my RH does.