Since Juan Pierre played his last game as a Dodger on June 29th, the Dodgers have gone 4-1 and look like a competitive team for the first time since Rafael Furcal went down. As much blame as Pierre (mostly deservedly) gets for the team being unable to score runs, his absence has nothing to do with the Dodgers recent success. Pierre has been replaced in the lineup by Delwyn Young and Andruw Jones and they've gone a combined two for 22 in their starts with a walk.
Maybe it's moving him out of the leadoff role that's helped? Nope, Dodger leadoff hitters have been almost as bad, going four for 22 with four walks for a .182/.308/.227 line. The Dodgers sudden ability to score runs isn't coming from an abscence of Pierre but from a sudden offensive surge by Andre Ethier and Jeff Kent who have been mostly silent all year. (Though I should note that Kent has an .866 OPS since he went down on May 26th).
Unless Juan Pierre was actively discouraging Kent and Ethier from hitting, his recent disappearance has nothing to do with the Dodgers winning. In fact, we actually kind of miss Pierre right now.