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From my understanding, airflow calculation in EnergyPlus(which DesignBuilder used) do not take any shading geometry into account. So you will not have any "blockage" effect from the shading geometry, if you need to study this effect, you will need CFD.
However, I think the simpler solution is to use a schedule to vary the opening fraction.
If you are using simple airflow method like ZoneVentilation:DesignFlowRate
or ZoneVentilation:WindandStackOpenArea
, you can use something like Opening Area Fraction Schedule
to enter a schedule that mimic the shading system operation to get the flow variation.