Can post nasal drip result in mucus entering into lungs and accumulating there, or does it just go in stomach?

Most to stomach. A little post nasal drip may try to enter the lungs & trigger a strong protective cough. If it went in with any volume you would have a significant pneumonia almost immediately. Most enters the esophagus/stomach & digestive pathway to be broken down over time.
Into the stomach. Mucus from the nose, mouth, and sinuses gets swallowed and digested by the stomach. The stomach processes it like it handles food and drink.