While more can be said, /u/commiespaceinvader's answer of theirs covers the rather pedestrian history of the Vienna Academy of Fine Arts during the Third Reich. This line of commiespaceinvader's answer is notable:

In looking through the literature, I could not find any reference to Hitler's thoughts about the academy once it together with all of Austria had become part of the Third Reich.

It is important to realize that his rejection from art school likely was not a major turning point for the young Hitler's life. If anything, his turning point would have been the his wartime experiences and the resulting chaos of the immediate aftermath of defeat. The Vienna Academy of Fine Arts and the sting of its rejection did not really animate Hitler's subsequent political career after his stint in the army.

Now Hitler was a person who kept grudges. Accounts like Goebbels's diary, stenographic accounts of military conferences, or Hitler's Table Talk show Hitler was not one to refrain from whingeing about past slights and how his success had vindicated him against his critics. The lack of any substantive comment against the Academy of Fine Arts suggests that this was not something Hitler took quite seriously. He certainly fit it into his autobiography as part of his self-created (and self-inflated) narrative of a rise from obscurity and it probably contributed to Hitler's dim view of Viennese cultural life. The latter was something Hitler had no reluctance expressing.

While it is unknown what would have happened to history had the academy accepted him, it is likely he would have washed out. For one thing, the school rejected him for a reason. While Hitler had some talent as a largely self-taught amateur, his paintings and drawings have real technical flaws. His favored artistic style of neoclassicism was quite out of date by the time of his application. Furthermore, Hitler showed both before and after his rejection a marked laziness in his work habits. He applied little of what might be termed self-improvement into his daily life outside of a few areas like public speaking or technical military matters.

Again, we do not know what would have happened had he been accepted. But his larger biography shows that he often chafed under authority and did not like his precepts being challenged. In the end, it is likely that failing art school would have had the same impact on his character as his rejection did.