Drag from the cowl flaps must be significant, did see a report years ago when a crew found themselves in the same predicament as this, feathered prop and fully closed the cowl flaps on the operating engine in an endevour to gain performance for a quick circuit while placing their faith in Mr. P & W to withstand the abuse. They made it
From recollection the cowl flaps were selected to the trail position (or takeoff/climb position, whatever it was called then) immediately before commencing the take off roll. The drag would be minimal. The difference between trail (or climb position) and closed was also minimal. Certainly in my time you would never take off with cowl flaps wide open and it certainly was never in the Ops manual for the type..
On one occasion at an Australian outback airport with no servicing facilities, we discovered the left engine upper cowl flap failed in the full open position while we were taxiing in after landing.
After discussion with our flight engineer, he suggested he mechanically wind the cowl flap down to the trail or take off position and lock it in place. We then taxied out on one engine until lined up for take off. We then started that engine and when the engine oil temp was within the lower limit for take off we departed and CHT remained normal for the remainder of the three hour flight. After landing we closed down that engine to prevent increase in CHT and taxied in on one engine.