Won’t be good. I presume that you are referring to breathing passage, not lung puncture as you asked about epiglottis.
Anything that blocks our airway can prevent us from getting enough oxygen and will make us choke. Choking is dangerous since oxygen deprivation can be fatal to a lot of organs in our body, particularly brain. In the first aid lesson we are taught on how to give immediate help when this happens.
I think that it depends how big it is, a little water would make you cough, also if you think about it viruses and bacteria can fall into our lungs and make us cough. If it is bigger we would choke as Theresia says
The body is designed to try and prevent this happening as much as possible so things like coughing or the gag reflex help you try and remove anything that might block your airway. Ultimately though, a big item would be very dangerous as it could stop you being able to breath.