Turfgrass water use is a real thing. The temperature-based growth potential (GP) is not real in the same sense. GP is a value between 0 and 1 that gives an indication of the potential for the grass to grow, based on how close the actual temperature is to the optimum temperatures for photosynthesis and shoot growth for that species. 

There are many practical uses of GP. I think GP is more useful than water use, or evapotranspiration (ET) as an estimate of water use, in the planning and prediction of turf nutrient use. 

But the water use is important. Nutrients go into the roots with water, so when lots of water is flowing through the plant, there will be more nutrients being used too. In winter, for example, dormant turf won't be using water, and thus there won't be any nutrient use. This has important implications for late autumn N fertilizer and how much of it is utilized by the grass.

As grass grows more, it uses more water. Or, as more water is used, the grass grows more. I'm not sure which is cause, and which is effect, but there is a definite connection between water use and growth. An experiment with grass in Thailand is illustrative on this point.

Bermudagrass, seashore paspalum, and manilagrass were grown in a plastic house in Thailand for 48 days. The water use and the clipping yield of the turf were measured.

This was a fertilizer experiment, with the same amount of N but different amounts of K applied as treatments. Looking at the water use and clipping yield, one can see that with more water use, there was more growth. Or with more clipping yield (growth), the grass used more water. This has obvious implications for how many nutrients are used and required by the grass.