No, quite specifically, Einstein's letter to FDR is what motivated the Manhattan Project. Hitler (parent's "austrian boi") may well have had a tremendous weapons program in the works, but Einstein's fear was motivated as much by what he knew of his colleagues in Berlin and the German zeitgeist(1) as anything to do with Hitler specifically. What Hitler wanted would have been trivia if it were not for the capabilities of the scientists who elected to stay in Germany during the rise of Nazism.

(1) what an awful yet accurate application of such a nice word, but I digress.