Can whole oats substitute for quick cooked oats in this recipe? How would the sub impact the final product?

In a pinch, I would make the sub. However, I think the texture would be thicker and chewier, not as thin and delicate as the original, and thus not as crispy either.
You can always turn whole (old fashioned rolled) oats into quick cook oats by pulsing the oats in a food processor about 4-5 times, until they are about 1/3 of the original size.