No, because the fatty has more kinetic energy, so each bump, although harder, is removing the same proprtion as the skinny guy losing a little bit of energy? The damper has to do far more work for Mr Chubby though so the may benifit from a longer stroke shock for the same travel to use more oil and dissipate more heat.
But…….
Haveing more travel would reduce the force on other components (assuming it doesnt just make him ride quicker and hit things harder), so more travel might save his wheels from being broken, but then the lightweight would probably still be quicker on an evenly matched bike.