I guess we didn't have any traditions to begin the year. However, in keeping with the title of your post, I think the relationships that are built between the parents and the players can only add to the enthusiasm and "team" atmosphere. My son's class had ten kids in it. The parents did things together in the off-season. Some of the dad's would play poker, some mom's go to dinner or a movie, we had cookouts, get togethers over a UK game, etc. The boys were constantly together doing one thing or another.
I highly recommend those types of bonding activities which naturally build friendships and contribute to a more supportive atmosphere for all involved - parents, coaches, and players.