Sprawl probably reduces productivity. When people cluster more tightly together, they become more productive -- this is known in economics as an agglomeration externality. This explains why the same person will produce more economic output in New York City than in a small town. Here is a picture of the correlation between city size and productivity ...
... Size gives an approximation of density, though some cities sprawl more than others. In fact, density itself is correlated with productivity, even holding size constant. So there is a big opportunity for the U.S. to take better advantage of agglomeration: increase urban density by making it easier for people to move into big cities.
I linked to the picture instead of reproducing the image here. Over the last three years or so, I've read a number of papers trying to make sense of the correlation between city size and productivity, as well as density and productivity. Suffice to say, the causal links remain contested.
Click on the "correlated" hyperlink and check out "Productivity and the Density of Human Capital." I've tracked the evolution of these literature reviews, which test the theories of Alfred Marshall and Jane Jacobs (to name two). I see two lines of inquiry. The first, and more popular, refines the correlation between city and productivity. Most people don't bask in the glow of the density dividend unless one is highly skilled and engaged in nonroutinized work. It gets even more specific than that, but I'll hold that thought for Pacific Standard magazine. The second line of inquiry tries to figure out how, exactly, bigger and denser cities boost productivity. I would like to see economists figure out the productivity paradox before trying their hand at geography.
To be diplomatic, we don't know if reining in sprawl and increasing urban density will juice productivity. Maybe it will. Maybe it won't. I doubt it will. But I can't prove my case.
Throwing diplomacy out the window, sprawl probably doesn't reduce productivity. Sprawl can be very dense, like Los Angeles. Highly skilled, nonroutinized labor can live in Connecticut and work in super dense Manhattan. Take a gander at the top 20 productive metros and draw your own conclusion: