I think I understand what he's saying. He's not saying that nosing over will find you some extra power you weren't making before, but rather assuming you've got a small but positive rate of climb, so you do have excess power available by definition. Therefore it is conceivable that you might be able to reduce your workload by trading a climb that really isn't getting you up very fast for a little extra airspeed so long as you're above the surrounding terrain. Obviously, if you weren't climbing a Vyse, this would go right out the window.
However, I think the improvement in handling qualities would vary from aircraft to aircraft depending upon how wide the spread between Vmca and Vyse is and the few extra knots you gain might not be worth it.