Yes putting eye drops in peoples drinks does make them sick and can be potentially fatal.
Eye drops are poisonous and will lead to diarrhea and vomiting and make the person very ill and it was sometimes used years ago as retaliation to some people who went to the bar and would not pay for their drinks.
Sometimes a bar tender would actually add a few drops of eye drops to a beer or other drink and then later on the person would get explosive diarrhea as well stomach cramps and be really sick.
Sometimes the person would have to go to the emergency room or urgent care for treatment if the persons symptoms got worse.
Putting eye drops in a persons drink should never be done because it can make the person really sick and possibly cause death as well.