Austrian here.
You are correct. After WW1, the leading political parties were strongly in favour of the großdeutsche Lösung, a unified (or "re-unified", as some liked to call it) greater Germany. The conservative catholic right had a strong German-nationalistic wing and the social democrats saw the unification of the Austrian and German workers as a step towards internationalism.

At the end of WW2, Austria's public opinion was heavily influenced by the allied's Moscow declaration of 1943, in which the 4 allies postulated the myth of Austria as "the first free country to fall victim to Hitlerite aggression".
This move had less to do with Austria's factual participation in the Third Reich's aggression and atrocities, but was declared in the hope to support the (weak) resistance movement.
When the war ended, the Austrian elites leaned heavily on the Moscow declaration in the hope to steer clear of any reparation costs. Austrians saw themselves as victims of Hitler's "demonic powers" and started to identify themselves with the idea of an Austrian nation. This Opferthese ("victim assumption") dominated the discourse on Austria's part in the national socialism era and changed only slowly until a new generation of historians (and political elites) started to discuss Austria's share of responisibility (Mitverantwortungsthese).