Well the obvious answer is yes, it will bring tempature down because the air in the room and the water in the res will want to equalize (to a degree). To what degree, I doubt all that much and youll be making the cooler work extra hard (but if you dont mind that energy cost then who cares). But water temp is extremely import with hydro so who cares if it doesnt lower the ambient temp in the tent...youll have the benefits of cooler res water which means more dissolved oxygen, better nutrient uptake, faster growth, and less chance of algae or root rot.

is your water temp ok right now? are the plants ok or suffering from the heat? leaves curled and cupped under? stunted growth? if your water temp is ok then for the cost of a res chiller, you could get a small A/C unit and just run it into the room and onto the res. if you get a good enough unit, this will enable you to drop 10 degrees F no problem both in the tank and in the air.