Evaporative cooling isnt efficient in a sealed chamber, it requires airflow. Also consider the temperature difference required to reach dewpoint and where the condensation occurs. As the droplets evaporate they will take energy from the chamber to achieve phase change from a liquid to a gas. Given the small amount of liquid involved it wont equate to much cooling, its not going to perfrom like an outdoor misting system where theres unlimited airflow. If the saturated air is left inside the chamber the only place it can condense is on the chamber walls and floor, assuming they are cool enough to acheive dewpoint. The wall or floor material will have at least some resistance (r-value) to the flow of heat so most of the sensible heat released as the water vapour converts back from gas into a liquid simply increases the chamber temperature.
If you want appreciable evaporative cooling, make the chamber walls and floor from a breathable material, assuming you have airflow across the outside surfaces of the walls and floor, water will condense on the inside surface. The sensible heat will be removed by the airstream, which in turn, cools the inner wall/floor surfaces. This results in an increased temperature differential driving the process. You can think of the liquid water on the walls and floor as waste, aka mist that didnt reach its target. If its running to waste anyway, you might as well use it to cool the chamber. Other bonuses gained from breathable walls and floor is automatic air pruning of roots, the breathable floor also guarantees total drainage. Root chambers with single point drains will always have some standing water, even with a decent amount of slope you`ll`have a few mm.