Because it's less humid, I can maintain a higher indoor temperature and still be comfortable, meaning the air conditioner needs to run less.
Do I use net less energy? In my case, yes, but your mileage may vary depending on your equipment, insulation, etc.
Your dehumidifier and your air conditioner are mechanically identical. The only difference between the two is where the waste heat goes. The exact same device is called a 'dehumidifier' if the waste heat is vented indoors and an 'air conditioner' if the waste heat is vented outside.
There's not really any efficiency gains from running a dehumidifier to reduce air conditioner use. They both use the same power and have the same effect on the absolute humidity, so you might as well just run the air conditioner (unless you want it to be warmer).
Before the dehumidifier I could get the room cool, but it still felt sticky. With both I'm able to keep the humidity at bay and cool the room as well.