Not really, I suppose historically it was more one of regional identity, the same as Bavarians or Rhinelanders. Austria and Prussia were essentially of equal footing amongst the German sates; the two big fish in an otherwise small pond. It was only with the Austro-Prussian war (1866) that the question of Austria's leading a united Germanic nation was solved in favour of Prussia leading the North German Confederation and Austria's exclusion from German concerns as part of the peace treaty.

Like you say about division by a common language, that plays again into the regional aspect. I lived in Swabia and learned a little bit of Swabish, which is almost nothing like the northern 'high' German. Austrian and Swiss German are also fairly different, but I've never actually met an Austrian to find out how much so. A Swiss tourist I met here couldn't understand me when I tried to speak high German to him though.

Sources: Berger, Stefan, Mark Donovan and Kevin Passmore. “Apologias for the nation-state in Western Europe since 1800.” ; Iggers, George G. “Nationalism and historiography, 1789-1996: The German example in historical perspective.” ; Berger, Stefan, and Chris Lorenz. Contested Nation: ethnicity, class, religion and gender in national histories.