Sounds like you want to know what percentage of the board's space is used up then. Consider it full when 80% of the total area is used up maybe? Something like this maybe?
percentage = (total area of balls)/(area of board - area of obstacles)
Chipmunk or CCPhysics? CCPhysics bodies have a property for their area. Calculating the percentage would just be a few for loops. Chipmunk collision shapes have an area property as well (in v7 anyway).