My kids have done Battle of the Books for years. I don't think starting a team would be a big deal. The coach has to be very familiar with the rules and teach the kids how the competition works. It probably would be helpful to have a second adult help keep score and organize.
In my kids' school, the battles are very competitive. There are competitions to determine the school representatives, then regional and state competitions. It's not really a book club in the sense that the object is not to discuss themes or characters. The object is to learn small details of as many books as possible and recall the details when asked. The questions are phrased "In which book..." and there may be a question about a very small detail of characters' actions, appearance, etc.
The kids who try out from my kids' school are the top achieving kids, despite the goal of the program which is to encourage reading in reluctant readers - these are kids who read prolifically anyway.
