It probably varies by ship. I know on some ships there are very few scheduled activities planned. I happen to have compasses for Indy right next to me and I only see 1 or maybe 2 activities scheduled each day for 18-20 year-olds. I'm actually planning on a cruise right before my son turns 18 just for that reason.
I would suggest going to the first scheduled activity on the first night just to meet people. So even if there aren't many scheduled activities they can meet people to hang out with.