No.
According to Jorhan Jumbl, a German army doctor who treated Hitler in World War I, Hitler did lose a testicle from a lower body injury in World War I. This may have contributed to Hitler's inability to reproduce.
Hitler's spouse:
In 1929 Eva Braun worked in Heinrich Hoffmann's photo store, helping to sell, take and develop photographs. At the time, Hoffmann was the dedicated photographer for Nazi Party Führer Adolf Hitler.
This is how Eva met Hitler and gradually developed a relationship with him, serving as his companion for a long time. She had just turned 17 when Hitler, 23 years her senior, had yet to take power in Nazi Germany, and she married him in April 1945 on the eve of his suicide, which she later shared.
Extended information
Hitler's World War I profile when he lost a testicle:
Hanzczuk recalled:
"It was 1916, and they were engaged in the fiercest Battle of the Somme, and for several hours Jokhan and his friends were admitting wounded soldiers.
He clearly remembered Hitler, whom they called 'The Screamer' because Hitler had a very loud voice and he couldn't stop screaming after he was wounded: 'Help me, help me!' He was covered in blood all over his abdomen and thighs, Hitler was wounded in the abdomen and had lost one of his testicles. The first question he asked when he saw the doctor was: 'Will I be able to have children in the future?'"
Baidu Encyclopedia - Adolf Hitler
Phoenix.com - Historical Fact: Hitler Lost a Testicle in World War I
Baidu Encyclopedia. -Eva Braun