Hitler can't rise to power in Germany without his WWI cred as a German soldier, period.
And I don't think Hitler can be Hitler in Austria, the place was just too laid back and beat down, though a Nazi type movement with Austrian characteristics is pretty interesting. The Austrian defeat is hard to characterize as a stab-in-the-back too, they just straight up got beat.
A Hitler who served on the German Eastern front instead of the Western front would be interesting. Would he still have the same complex of views about the Jews and the Slavs? Would he still have his famous aversion to chemical warfare, and his embrace of technologies and tactics designed to avoid trench stalemates?
No, it's easy to justify a stab-in-the-back legend in Austria; blame it on the Hungarians or Serbs, or Croats, or any other minority group or combination thereof. There's no shortage.
I agree that he can't rise to power in Germany, but a highly revanchist Austria under his rule might be very interesting in the post-WWI period. He would be a close ally of Mussolini, assuming Benny comes into power at roughly the same time. Benny would be appreciative of any ally against Yugoslavia, and I'm sure Hitler would love any military aid he could get against Czechoslovakia and Hungary. There's probably a German minority in Yugoslavia to liberate, as well.
He would probably hate Slavs more than Jews, so any potential Holocaust might be more focused on Poles and Russians rather than the Jews. It would be much more limited due to Austria's limited resources and reach, fortunately.