Here is my "analysis":
Assuming the board is not in a board bag and it is placed upside down on the car roof rack, there will be a pressure differential when air passes over and under the board, hence there will be a lift force in the direction of the hull (is it called hull?, the bottom of the board).
With the nose pointing to the front, there will be more drag than if the tail is pointing to the front.
However, if the board is placed with the deck facing up and nose pointing to the back, the pressure differential will press the board down onto the roof rack, hence less force on the straps (lesser risk of strap breaking?)
2 other disadvantages of putting the board upside down:
a. the roof strap might cause depression marks on the hard edge of the board if straps are pulled very tight. (eg, slalom board)
b. risk of flying pebbles hitting and damaging the bottom of the board which you want to keep it smooth. (Deck of a board will be easier to repair if damaged)
However, I'm not sure if this drag & lift is significant with regards to fuel efficiency and when the board is transported with a boardbag. : )