Because this summer and fall have been so dry, I recently contacted Dr. Joe Brummer, of CSU Crop Sciences, to see if fall irrigation would be beneficial for the plants.  Joe gave me thorough, interesting, and educational answer.

Joe said, "If your grass is already brown, you should NOT put the water on it." 

Brown grass is already dormant, and putting water on it will will wake it up and cause it to use its carbohydrate reserves to start photosynthesizing and growing again. 

The plants will then naturally go dormant again in just a couple weeks due to cold temperatures.  When spring comes and warm temperatures bring the plants out of dormancy, they will rely on their carbohydrate reserves to start growing again.  If the plants were brought out of dormancy this fall by irrigating them once they were already brown, their carbohydrate reserves will be depleted and it could stunt their growth next spring. 

On the other hand, if your grass is still green right now, it is okay to have irrigation water on it. 

Green plants are still photosynthesizing and increasing their carbohydrate stores. 

They would not be using their reserves to start greening up.  That being said, you should be aware that dormancy is a natural progression in the life cycle of grasses, and they should be going dormant soon anyway due to the cold temperatures. 

In conclusion, in the fall, it is okay to put water on green grass but not okay to put water on brown grass.