Correct. It will behave stiffer. Going from a cut past center to a cut to center bow is like moving the side plate out, which requires a less stiff arrow or makes the same arrow act stiffer.
Just so we're on the same page. When you say your bow is cut 3/16 past center, you mean it's cut 3/16 to the right of the center of the bow (on a right handed bow), correct? If the shelf/side plate is cut 3/16 to the left of the center of the bow, it's called proud of center (for a right hand bow).