As were both John Banner (Sgt. Schultz) and Leo Askin (General Burkhaltar). Ask in came to the US in 1940 and served in the Army Air Foce during WWII.
I think it was the ultimate joke on the Nazis to have all the major German parts in Hogan’s Heroes played by Jews, who supposedly all had hooked noses, according to the Nazi propaganda of the time.
It reminds me of the testimony of the Auschwitz commandant, Hoess, about how at first he was shocked how “German” the Jews that were going to the gas chambers looked.