There probably aren't too many bows that can stay in a 4" circle with a single pin setting. How abouts we change the parameters a bit. Hows about we say 4" up and 4" down from center. That would be approximately top to bottom of the lungs on a deer.

With a 360gr arrow doing about 280 fps it might be possible. You'd probably have to sight the pin for about 28 yards. I've done this with bows shooting about 260 or a tad more, set for 25 yards and had about a 4" drop at 32 yards. The highest midrange point was just about 2" high at 18 yards.

The only real world way to find out is to get out and do it. See what you get. Charts and computer programs might give you an answer, but they don't take into consideration such things as wind currents,air densityand such.