No, not really. There are no sources supporting the assumption that the rejection of his application to the Viennese Art Academy was an important event in Hitler's biography. Furthermore, although commonly referenced, the 'inability to be admitted to an art school' was more complex than it is usually portrayed. Adolf Hitler applied for admission to that school in 1907 twice and was not accepted (not the same thing as being rejected - as in most European universities, the number of students were limited and other candidates were found better). He was not accepted to a painting course, however, and the commission, noticing that Hitler seems to a talented draughtsman with some experienced offered him place on an drawing course at an architecture faculty. And here Hitler fell victim to a combination of his fate and own life choices.

Aforementioned faculty, considered to be more 'technical' part of the art academy, required finishing the Technical upper secondary school that in turn required the Matura (also Abitur) or 'maturity exam' every student of the secondary school had to pass to be admitted to any further academic or technical university or higher secondary school. Hitler however, dropped out of Realschule (general lower secondary school) in Linz after showing severe downgrade of results in 1903 following a sudden death of his father and having succumbed to a serious pulmonary condition (possibly pneumonia) shortly after. After recovery, Hitler though he took up education in another Realschule in Steyr, he finished it without taking the maturity exam.

According to Hitler's own words in 'Mein Kampf', the results of entry exams were not necessarily a blow to his ego. He admits that he learned something about himself, as he did not fully realize that his drawings are much better thank his paintings. He also admitted that after the conversation with the Dean and the commission during exams he simply decided to become an architect or a construction specialist (he uses the term 'Baumeister' in his book). But at the same time he realized that lack of technical education makes him ineligible for architecture studies and lack of maturity exams make enrollment into technical school impossible. This could have still be circumnavigated by taking extramural education, but Hitler lacked finances to do so. In 'Mein Kampf' Hitlers states that the results of the academy exams and realization of his errors caused him to be 'unsatisfied with himself for the first time in his young life' but then he states that he soon 'regained inner calm and determination [...] inspired by his father who came a long way from the son of shoemaker to a civil servant'. And this is everything he ever writes about this episode of his life.

In his autobiography, Hitler attributes the development of his antisemitic stance solely to the analysis of the political life in Vienna and the relation between Austrian and German policies. Initially, Hitler was rather ill-disposed toward social democracy and while he supported many socialist ideas, he though that the contemporary social democracy and other socialist parties use what he considered a half-baked solutions or are simply hypocritically vying for power with little real concern for the people they officially represented. Additionally, he noticed that 'international' press quite commonly praised France while at the same time criticizing Germany what did not set well with Hitler who considered himself German, both ethnically and culturally. Then, he states that he finally noticed that in his opinion most if not all of the publishers and prominent journalists of the socialdemocratic newspapers, as well as a lot of journalists in the international ones are Jews. This apparently corroborated the notion that he Jewish politics are opposed to the politics of Germany and, to some extent also of Austria and are to large extent aligned with social democracy. Hitler himself noted that such observations caused him to treat Jews not as simply one of many religious groups in Austria as he did previously (he notes that anti-Semitism was something very rare in Linz) and started to treat them as a group with distinct political interests. Further exposure to the anti-Semitic and Pan-Germanist rhetoric only strengthened the notion that social democracy and internationalism are both detrimental to German raison d'etat and aligned with Jewish interests and thus Jews themselves are inherent hostile to German nation and its interests. Such ideas slowly gained traction in Germany, to coalesce in 1918 in the form of 'Dolchstoss' (stab in the back) rhetoric, blaming Jews for sabotaging the war efforts of Germany and ultimately contributing to its defeat in the Great War. Such rhetoric was widely used by various nationalist groups, including German Labour Party formed in 1919 by Anton Drexler and Karl Harrer with the support of the Paul Tafel, member of the Thule Gemeinschaft. Then, a certain young informant of the Reichswehr is assigned to observe the meetings of DAP to check whether they pose a threat to national security. The rest, as they say, is history.

To sum this up, Hitler's anti-Semitism seems to not be based on any events in his personal life and is purely a product of his political leanings and inspirations that largely developed in his early twenties, using his nationalist and pan-Germanist tendencies he subscribed to in his youth.