My initial days of running had a dramatic positive effect on my productivity. However once my body got used to running I see no difference. I must admit I have stuck to the same pace and distance more or less. 5k in about 35 mins.
I wonder if some of it has to do with perception. When you begin a new habit, or change up your routine, time seems to go a bit slower than usual, and thus maybe you feel that you are more productive?