As pp mentioned, you are correct in assuming that you can drop off and pick up anytime during the open hours.
When my children were in the club, I remembered asking something to that effect. I was told that as long as it's during the normal open hours, they don't turn away the children. They did mention that sometimes during Open House, it may get busy and they may ask to wait, but very rare. I would also assume if there is an issue with the club, they may close it down for repairs, but other than that, I was given the impression that they wouldn't be "full". In all the times we brought my children over, we've never been told to wait....even during popular activities.
I suppose this is the reason for ensuring they don't go over the total number of children per cruise. They don't really want turn any child away based on capacity.