My climbing partner is really fat. If he is following a pitch quickly, and falls with a loop of slack at his knees, will that fall shock load the rope?
You two sound like a dysfunctional couple. Your partner can’t control his weight and you can’t belay well enough to keep the rope snug. I suggest you look seriously at those two, larger issues, and not worry so much about shock loading the rope.
Just what is “shock loading,” anyway? You can argue that all falls shock load the rope, because the rope instantly goes from not being loaded to being loaded. Shock loading, per se, applies to falling on static webbing and ropes, such as daisy chains and static cords. In these cases the webbing or cord doesn’t stretch, shocking the anchor (or you or your belayer) with an instant peak load, which is dangerous to the point that it can cause anchor failure or rearrange your insides. Compare that shocker to the relatively mundane dynamic loading you’d get with a stretchy climbing rope, regardless of whether you are toproping or leading.
Vernacular aside, you never want slack to develop between someone toproping or following, or the anchor and the belayer. The slack will cause the climber to free fall as if he was leading, which defeats the purpose of toproping. For a loop of rope to appear at your seconding partner’s feet, you’d have to have about five feet of slack in the rope. He’d drop about two and a half feet before coming onto the rope. That little fall by itself isn’t going to generate a dangerously high load, but why risk it? Falling like that on toprope is unnerving, exposes the climber to hitting a ledge, and is sloppy, bad form. Get your finger out of your nose and quit being a slacker.