the rule of thumb for passive intake is you want it 2-3 X larger than the area of your exhaust
so 12.56 is the area of a 4" pipe
doubling that is equivalent to 6" (2x larger) or 8" (4x+ larger) would make the fan not have to work as hard.
I agree as long as the extraction fan runs and you have a few passive intakes it will suck a vacuum on the chamber