I guess it sort of depends. That's always my main concern with constant fogging blasting directly into an enclosure.
Also, it is good for the cham to be able to take a nice shower from the misting, they get to clean their eyes, etc, which is a benefit of doing the misting.
The bottom line is if you run the dripper, and run a humidifier (but don't blast into the cage), and are confident that your chameleon is drinking and showing good signs of hydration, then I think you would be okay. Just make sure the cage gets a chance to dry out between humidifier use, and you aren't getting things too humid.
I would still recommend misting over a humidifier, and rely on the humidifier to supplement ambient humidity. Of course all of this depends on species, as they do have varying requirements.