I have always supported the Sydney Swans and love singing the team song at the end of the game when they win. My son plays junior footy and we encourage his team to sing their club song after every game as well. it definitely builds cohesion when combined with training and socialising together. The common uniform is also a big part of identity building.
For further thought though, my daughter has been part of a team that had a uniform and a team song, but didn’t have time to train together or socialise together as they came from many different schools, and there was almost no cohesion in that team.