Though cough drops will not cure your cold or sore throat, they will help when taken as needed. Menthol will soothe and fruit flavored will add vitamin C plus calm the throat. There are many different brand cough drops, but some work much better than others. You need to try brands to see what works best for you, but they do help. ..Especially if you have a tickle in your throat or a nagging cough.
There is nothing magical about cough drops specifically that stops you from coughing. Sucking on any hard candy will basically have the same effect, soothing an irritated throat. Sucking on candy or cough drops produces saliva that moisten the throat. Some cough drops contain zinc and vitamin C which might give a slight boost to the immune system. Menthol gives a cooling effect to relieve the "scratchy" feeling. Drinking plenty of water or juice helps soothe the throat as well.