Is it possible to eat a boiled egg and throw up whole?

No. The esophagus sphincter connects the esophagus and the stomach. It normally remains closed, preventing the stomach contents from regurgitating into the esophagus as long as it functions properly. When a person throws up, the sphincter relaxes and opens to let the stomach contents evacuate out of the body. Any digested material, such as a fully digested boiled egg, will not remain whole but be partially broken down into food particles.