That's the wonderful thing about geometry, I don't have to do the experiment to know the answer. Rotating the gravity vector 45 degrees to the rear will not change the relative position of the hands, hips or feet, nor will it change the direction of the force vector on the chainring. Since gravity plays no role in a balanced system, there will be no additional forces on the legs or cranks from the change in gravity. All this adds up to no change in muscle recruitment to move the pedals against chain resistance.

On the other hand, body weight will now have a component parallel to the frame and back which must be opposed. This can be from some combination of friction with the saddle and pulling against the bars with the arms. Hold on. If body weight is constant and some of this force is directed longitudinally when the wheel is raised, doesn't that mean there's less weight on the saddle? Could I be on to something? Could it be that people raise the front wheel to be more comfortable by reducing weight on the saddle? And as long as the angle is slight, this could come at no cost since saddle friction can supply the force?