I used to be on a team where one of the team members had a certain medical condition. One or two people knew about it but as a general rule, they made a point to keep it completely confidential. They wanted to be judged by the quality of their work like everyone else, not by doing "good work, for someone with condition X". A group outing was scheduled at one point, and the logistics and venue of the event conflicted horribly and unavoidably with that medical condition. The team member was left with a couple of options:

1. Attend the event, and have everybody learn about their medical condition.
2. Out themselves to their manager and ask if the event can be changed.
3. Skip the event and have the rest of the team see you as that one weirdo that doesn't like to spend time with them.
4. Try to make up some convincing-sounding lie to avoid the event, and miss out on everything that happens.

These are all bad options with consequences. The first option would result in the team member being subconsciously labeled as someone with this particular medical condition, forever changing everyone's perception of them and expectations for them plus opening the door for being illegally discriminated against in the future. The second is the same but potentially more limited in scope, provided the manager could be trusted to keep their confidence. The last two force the team member to miss out on whatever the group gets to do, and can make them look antisocial (or worse). It's a no-win situation for the person involved. In this case my team member chose the last option. The lie wasn't very convincing, and it impacted their social relationship with other team members for quite a while.

To answer your question yes, you should say something. Your employee has trusted you with this information, and you should do what you can to protect him from situations where his medical issues might cause him unwarranted harm in the workplace. He doesn't really have the ability to do anything about it on his own. His only way out is if he can be in that sort of environment without affecting his recovery. You don't know if that's the case and asking him about it would be invasive (you may not even get an honest answer). The consequences for him for a bad assumption on your part could be beyond devastating. I definitely would not sit back and hope it works out.

There's really no need to talk to the employee, talk to the event organizer. A tactful message to the event organizers could be something like this:

Can we please de-emphasize the role of alcohol in the upcoming event? Not everyone can/does drink alcohol for a wide variety of reasons, and I wouldn't want anyone to feel singled out, pressured, or unwelcome.

Don't mention names. Don't mention reasons. Don't even mention the number of people affected. Your message is "this is a problem that likely exists in a group this size, please keep it in mind and don't let it spoil anyone's experience". That way you're covering anyone with medical issues, religious issues, interns under the drinking age, even people who just choose not to drink and don't want to be hassled about it. Just don't include anything that might remotely point back to a specific person. Aside from the potential legal liability for sharing confidential medical information, you don't want rumors that so-and-so is pregnant, or can't go into a restaurant that serves alcohol because they're on parole. Honestly, this is a reasonable position to take even if you didn't already know that a team member might have a problem.

The only time I'd recommend talking to the employee about it is if the event organizers won't play along and if your company culture is such that there's a good chance that drinking will be a significant focus of the evening. Don't ask them to divulge any information, just warn them that this will be a drinking-focused event and let them know that you're here to support them in whatever way they need. I definitely recommend that you don't drink during the event, so that your team member doesn't stand out. Be prepared to give them plausible cover if they say that attending would be a problem, like giving them a last-minute assignment to cover a (fictional) phone call with an overseas client/supplier in a drastically different time zone, or put them in the "on call" rotation that night in case your automated systems encounter a problem. Better for you to look like the mean guy that made someone miss the party than for them to be forced into a damaging or dangerous situation. I've even seen situations where the person who needed accommodation volunteered to help at the event in question; it was obvious that they weren't participating in the problematic activity like the rest of the group, but nobody thought twice about it. They're just participating in a different way.