We just got off the Legend of the Seas and my son (just a few months shy of 21) was faced with the decision if he wanted to drink beer and wine. Joanie (my wife) had to make the decision as the parent. For passengers between the ages of 18 and 21, the parents must agree to allow them to have access to beer and wine. When they issue the sign and sail cards, one hole means, yes they can have beer and wine and two holes means no, they cannot.
Since our son does not drink (straight edge, I think they call it) it was a none issue, but rest assured that you will have a say in the process.
Now, in the ports is another thing. We had a group of high school kids who got so drunk in Cabo, they had to be carried back onto the ship. I guess it just depends on the kids.