Can you die from eating too many cough drops?

There are a lot of unknown variables in the question to give a really good answer. If you are talking about over the counter regular cough drops that are not medicated, then if you are otherwise healthy (e.g., not a diabetic), a whole box would be no more deadly than eating a lot of candy. You probably would get a sore tongue from the hard candy.

If, however, they are medicated cough drops, then you would need to follow the label directions on how many you should use in a given time period.