You are suggesting that the down wing has increased drag. Yes, that is another way of saying that there is a moment created about the earth-z-axis. That must indeed happen if the aircraft is to yaw. But why that increased drag? The wing is going slower and has less lift; why should the drag have increased?
If you (pilot)shift yourself to the left so you hang further under the left wing, then you yourself will create more drag on that side of the aircraft than was there previously, plus you will alter the C of G to the left, so bank left.