(not a definitive answer - just poking around)

I don't have DesignBuilder, but ran both IDFs (noA == "no awning", vs A == "awning") with E+ 9.5, for a similar climate. August results for Zone 1, Wall 4 Window:

• Surface Outside Face Incident Solar Radiation Rate per Area: noA (135 W/m2) vs A (120 W/m2)
• Surface Window Transmitted Solar Radiation Rate: noA (165 W) vs A (114 W)
• Surface Window Heat Gain Rate: noA (115 W) vs A (123 W)

Incident and transmitted rates are what one would expect. Yet the overall window heat gain rate is indeed greater with the awning (+7%). If the awning is left permanently deployed in August, then this increase could be explained by a lack of radiative cooling at night; a permanent awning would in part hinder the window from seeing the night sky. A detailed hourly comparison of diurnal vs nocturnal window heat gain/loss rates (or dynamically retracting the awning at sunset) may reveal this ... but I'm out of time :[.