Yes you do but i have seen people only use a fogger because it creates a morning dew effect and all the leaves have a lot of water on them. I personally would still at least have a dripper run for at least a half hour two times per day. You can create a dripper by putting a pin whole in the bottom of a large cup the bigger the hole the faster the drip so you know the drip doesnt have to be fast.
it depends on how much water it creates for your chameleon to drink off the leaves and branches. Do you see him/her drinking after you run the fogger? How often are you running it?