Ok, let me clarify my previous statements...
During the school year we can have practices within the context of last hour PE class. A student must get the varsity coach's permission to participate, but usually it is not a problem. On some days, students are held over 45 minutes to an hour for extra workouts like weight lifting...
There are fall games, but these are voluntary with no requirement to participate...however, it is always wise to participate unless you are involved in other in-season sports. The summer league is where the coaches get a better view of the students and if you want to play in the spring it is highly recommended (my opinion), although it is not required to participate to make the team.
The varsity coach where my kids attend primarily uses the off-season to build core strength while incorporating some throwing...
I like your California way of doing it because you can keep your team together and work at making it stronger by competing in tournaments and practices.