The Mayan ruins on Cozumel are at San Gervasio and are not especially good. Plus the place has mosquitoes - lots of them. Nothing quite like being half in the bag, sweaty, and fighting mosquitoes in a jungle, right?
I've also seen people so wasted they were on all fours crawling back to the ship from Carlos 'n Charlies. In those two events the ship's security did take control and I think those people were confined to their cabins until the next morning. They do have an obligation to ensure your safety as well as the safety of the other passengers.
If it's legal - and it is on Cozumel for you - then have a fun time and a few beers. Just don't be one of the human sand crabs I pass by on the pier.