Nah. Here's Bruce Timm himself explaining:Batman TAS was that but Caped Crusader looks like they went all the way with the 40s.
"We’re intentially avoiding direct references to ’Real World’ figures and events of the 1940s (World War 2, Presidents Roosevelt and Truman, nuclear weapons, Stalin and the expansion of the Soviet Union, etc) in order to keep the time period somewhat vague. CAPED CRUSADER takes place in a elastic Time Bubble, anywhere from roughly 1939 to 1950."