I have been reading about past Olympics and found out that the DDR had a systemic doping program, (especially in Munich in 1972). Given so much was riding on the 1936 Berlin Olympics, such as Hitler's ideas of Aryan supremacy, would the German team have used performance-enhancing drugs?
EDIT: By doping I mean to take drugs that would improve an athlete's performance
Not a complete answer but some facts:
Steroids weren't marketed commercially until 1960 however have a record of being used in sport since at least 1954 (Soviet physicians talking to Ziegler)
There is definitely an element of the definition that the substance needs to be banned to be considered doping.
There has been a tradition of using substances since antiquity.
In the Berlin Olympics in 1936 amphetamine first made the scene to a notable level.
In 1988 Ben Johnson was stripped of his medal for steroid use. I think this is the first case of steroid use resulting in a high profile penalty.
It seems certain that the answer to your question is subjective based on the meaning of doping. I don't think a case can be made that any of these examples went against a ban from a governing body. I don't see that there was any specific international agreements in place at the time that would prevent performance enhancing substances from occurring and it doesn't seem like this is an organized practice until the Cold War started. I suspect that view might be a tad naive as there are credible pieces of evidence that several actors were,in an organized way, supplying their athletes with substances.