Team synergy results from a combination of factors, not simply from the fact that players get along with one another (who can forget the 25 players, 25 cabs era of 20 years ago with the Clemens Red Sox?!?). Synergy derives from good team design. That means selecting complementary parts, not simply assembling all-stars based on statistical models (sorry, Theo). It also means thinking about who your team leaders will be, and how they will lead through both words and actions. Finally, it means not overreacting to a small sample of poor performance. The Sox didn't let one bad year cause them to forget the longer term pattern of strong performance for players such as Lester and Buchholz.
Synergy also involves creating the right environment in which people are motivated to excel. John Farrell has created an environment of collective accountability. He's also been transparent, communicating his decisions and rationale to players clearly and firmly.
What about the beards? Well, they are fun. They are a wonderful bonding experience. In the end, though, the team design and environment matter most.