No, your stomach acids are designed to counter the mild acidity of a Coke's phosphoric acid. It's no more harmful to your insides than the citric acid in orange juice.
Metal left in Coke will cause a chemical reaction and thus "dissolve" some metals. If you drip Coca Cola over the center of a tin/alluminum can, after a day you'll only
see the plastic internal lining of the can -- the coat that protects it from disolving the can internally. Pretty neat stuff.