Would be particularly interested if any administrative staff or the director knew about Hitler's rejection and then had to watch his "secondary career" unfold after World War I.
Bonus Question: What happened to the Academy after the Anschluss?
I have now written about the Vienna Akademie der Künste a couple of times here and here and as far as I am aware from the literature, nobody from the academy every publicly commented on this matter.
After the Nazi take over of power in Austria in 1938 there were, of course, changes implemented in the Academy, the most notable one, a complete purge of all personnel and students that were Jewish or known to be politically anti-Nazi. Immediately after the so-called Anschluss in March 1938, the Vienna NSDAP put three new men in charge of the Academy, Ferdinand Andri, Wilhelm Dachauer and Alexander Popp. Interestingly enough all three of them were aesthetically and politically close to the Vienna Secessionist group and had in the past had personal ties to Klimt.
The person who was mainly responsible for rejecting Hitler, Christian Griepenkerl, died in 1912 of natural causes and I would expect that in the about 30 years it took from Hitler being rejected from the school I would expect the to have undergone a severe change in personnel, especially with WWI happening in the meantime.
After Anschluss, the Nazis immediately began a purge and in the first days after March 12 already 13 Jewish professors were let go from their posts (almost everybody working at the Academy was a state employee since the Academy was and still is a public university run by state employees). Furthermore, the trio (of which Popp later became chancellor of the school in 1941) prepared a manifesto about what was in store at the academy. The new program consisted mainly of pushing a more "German" style of art, cutting ties to previous more abstract art styles within the academy and place a larger emphasis on the monumental. It basically lead to what we today recognize as typical Nazi style of art being thought.
What is also interesting and has only been revealed by recent studies is that the Academy "lost" only 20% of its personnel and only 7% of its student to the Nazi purges. This means that by the time the Nazis took over in Austria, Nazism was already a rather present force within the academy, especially its students. In light of all this it is hardly surprising that the Academy retained its prestigious status and continue to move forward, albeit with a slight change in the art style that was taught as prominent.
That academy has been Nazified leading up to the war and especially during the war is also apparent by the subsequent denazification efforts. While at first, a third of the staff was let go for either being not Austria or a member of the NSDAP (all in all 30 people, 23 of which for NSDAP membership according to Pawlowsky), most of the latter were soon pardoned after the Austrian ex-Nazi legislation of 1947 and some were indeed reinstated. Also, rather than replacing them with returning Jews, they were mostly replaced by former students who had not been members of the NSDAP or Austrian artists who had spent the war in "inner emigration", i.e. had stayed and worked on.
How ineffective denazification was among the student body is exemplified by the so-called "Klosterneuburger Strandbad Affaire" (the Klosterneuburg bathing beach affair). At the public bathing beach in Klosterneuburg (a town near Vienna) nine young people, including five students of the academy, had formed a swastika from their bodies and photographed it from above. The court in charge of their trial chalked it up to teenage shennanigans and they were let go but the fact that two years after the war was over, students of the academy were still in part Nazis gives a pretty clear picture that the ideal of denazification was not working in this case.
Sources:
Verena Pawlowsky: Die Akademie der bildenden Künste Wien im Nationalsozialismus. Lehrende, Studierende und Verwaltungspersonal. Vienna 2015.
Oliver Rathkolb: Nationalsozialistische "Kultur"politik in Wien 1938-1945.