No, true enough, they didn't. Hitler played off the revival of scientific racism and eugenics that emerged in the 1910's and 20's, a full generation after Darwin was dead. Hitler did indeed appeal to (an overextended analogy of) evolutionary "struggle" in support of his militarism. So did German militarists in WWI, as William Jennings Bryan correctly noted.
But, interestingly, Hitler tended not appeal to evolution when it came to his racism and antisemitism so much as he did "laws of nature" ultimately attributed to the "will of the creator" (see my previous post to you about your quote from Mein Kampf). In fact, the official Nazi philosopher of racism and antisemitism, Alfred Rosenberg, in his Myth of the Twentieth Century spoke of racial purity in connection with the notion that each "nation" had been created with it's own particular "soul". (Granted this sense of "creation" was mystical rather than literal.)