We have maybe 50 dives in Cozumel over 3 years so I'm far from expert. I have never seen a down current but I did get caught in a ripping lateral current in April. When we dropped in, it was like a sandstorm. Visability was far reduced from the normal clear as air Cozumel standard. We were South of Columbia Pinnacles and where we dropped it was a pure sand bottom. The current was stirring up the sand and it was beautiful, like a snow storm under water. My wife saw some swirling "tornadoes." We drifted (fast)to the pinnacles and we went through a swim through. I got separated from my group when I saw a set of fins on the other side of the reef and followed. I immediately saw that it was not my group (different tanks) and went up 20 feet to look for my groups bubbles. As soon as I got above the reef, the current that was hitting the reef was accelerating as it went over it. There was no fighting it so I went for a ride. I launched my SmB and did a normal safety stop. By the time I was done the boat and my group were there to pick me up. Other than a missing $25 dive light and a scratch on my hand, all was good.
That is the only time we have had an issue. Other than being horribly embarrassed by cutting everyone else dive short by about 15 minutes, it was still a great dive. I bought some lunches for those that were hungry during the safety interval and some drinks when we returned to the dock to make up for it. It was startling how fast the current was, but I had an SMB and reel and I knew every boat would be looking for me as soon as my group surfaced.
Yes, currents do happen, we were on an intermediate/advanced boat, and the currents were obvious as soon as we dropped in. Your DM will know of your skill level after your first dive and will adjust your dives as needed. Your not going to Devils Throat on Day 1.
We went back the next day and did the same dive and it was amazing. The reefs were dusted with sand and it was absolutely on of the most beautiful dives I've ever been on.
concern is good, it keeps you safe, check your gear yourself, check your buddy's gear, check your own nitrox, and thumb a dive if it doesn't feel right. Before my adventure, I did ask about down currents and was told swim to the wall.... I never thought I would be doing a lost diver drill. Not every dive will go as planned, that's just a fact. I still won't hesitate to take my family to Cozumel for a dive vacation.
Make sure you have an SMB and a reel, (there is statistically far less than a 1% chance you will need it) and get ready to have a new favorite dive spot. Cave diving, Atlantic wreck diving, ice diving.....now that scares me! Cozumel reef drift diving....not at all.
Safe travels,
Jay