Vaughn injured his ankle and suffered through a disappointing season. Naturally, the Angels' chemistry collapsed along with their won-loss record. The team came close to revolting against Terry Collins' hard-handed style of managing, openly complaining when the organization began discussing a contract extension with him. Collins got his contract anyway, the team continued to play poorly, the clubhouse atmosphere continued to disintegrate, and Collins got canned just weeks after he was given a vote of confidence. That's not to say that the atmosphere in the clubhouse is completely irrelevant.
Bad chemistry can still be destructive.
There has never been a manager in history that led his team to the playoffs without commanding the respect of his players. Dick Allen was one of the best hitters in baseball in the 1960s and 1970s, but he was considered such a disruptive influence among his teammates that it's debatable how much he helped his teams. That's hard enough to identify, and almost impossible to keep bottled up for long. The problem stems from the real definition of chemistry. It's not just a team where everyone pulls for each other and the players share cabs back to the hotel.