Well obviously. Be sensible now. Carrots are very good for you, but if you eat too many you'll die of carotene poisoning! Extreme examples are a mostly waste of time - I could equally say trim your handle down to 10mm diameter and see how much control you have over the bat.
Unless your hands are properly tiny (maybe they are, who knows), adding 2-3mm to your handle clearly won't affect your ability to grip it. If you want to get into it, logically there must be a perfect size for optimum grip force, and a point at which it is too thick to grip properly. This clearly is not the same for all people, as people have different size and shape hands. Bat handles must be useable for people with the smallest hands, so clearly for the rest of us there is room to play with. Forget the biomechanics side of it, IF your hands are not so small that it causes you to lose control of the bat, having more shock absorption and more leverage at your point of contact with the bat will clearly enable you to hit the ball harder and more precisely. I'm assuming that someone unsure whether to use an extra grip isn't currently wavering on the point of losing control of their overly thick handle, so the idea of not being able to control a megahandle isn't too relevant.