It uses the humidity in the air, so it's possible that with a larger number of these in the area, the humidity would be reduced to a point where there is none left to remove.
The Earth is enormous, it would take a staggering number of these to make any dent in humidity, and even then it would be a local dent only.
Don't forget water is a closed loop - this water they consume is also eventually returned to the environment (sweat, etc.), where it evaporates and restores the humidity.
Would be nice if you could just pull a cloud or two down from the sky.