I stumbled on this recently and you may find it valuable too (how the different carb levels affect you)
So to answer your post' title question: No.
To answer, "Will I see any benefits at all from the less-carbs aspect of my diet" -Yes, anything from better health to weight loss, depending on your intake.
As to, "or will any benefits be based much more on what I am eating rather than what I'm not?" I think the answer is also yes, as you will be affected (either positively or negatively) by everything else you eat.