Yes, camping at the site B is allowed, up to 14 days. It is actually on the National Forest lands at the parking area. Currently there is a fire ban in the area, if you have a fire permit, you can have a camp stove, but no open fires are allowed right now.
The formal names for the two sites, B is 'Freedom Trail parking area'. A is an old 'Hunters parking' which lays behind a fence. Your FJ will make the trip to Freedom just fine. I recommend when you reach the area, there are two good camp areas, one on the right side down in a gulley and one on the left which is more exposed but off the main trail.
And, as always, ensure you take plenty of water and snacks, the area is cruel to the unprepaired.