Yes, but ONLY on direct trains that do not stop in DE. These are RailJets by OeBB.

BTW: IF you have more time and want to see more nice mountains: then the old route via Bischofshofen-Zell am See is much nicer, but takes longer and I am not sure if there are even direct trains on it all the way.

You can ALSO pass DE on connections from Innsbruck to Reutte, via Garmisch-P. In the past there were a few direct trains (no change), but I think that is no more.) In the distant past, when one had to show passpt/ID at border for checks (before Schengen common zone came) these connections already existed and the AT-trains were kind of ´sealed off´ to pass the foreign lands, so that no illegal entry could happen-in theory.

An Austria Pas is also valid via Lichtenstein (so you can add 1 more country visited ( till first stop in Swiss.

 Oh-as I now see vous etes FR-ancaise: the 1 country pass is what it says (in this case not exact-see Lichtenstein), it does NOT cover the trip from your home to Austria. It seems that esp. the Francais are quite confused about that-every week same questions.

Thanks for your answer :) 

So I have to check if the train stops in DE. 

We are going by plan in Austria and then using our pass.