If you use one of the direct trains without stop in Germany, then you can use the Austria pass.

Thank you rvdborgt for your answer.So,Have you actually done this ‘going from Salzburg to Innsbruck pass through Germany,and useing the Eurail Austria Pass’ ?

Yes. All non-stop trains (RJX from ÖBB or Westbahn services) through that bit of Germany are operated by Austrian companies and Austrian tickets are 100% valid.

This corridor is in place for more than a century as it's a huge shortcut between Innsbruck and Salzburg.

You don't pass through customs or anything, it's like travelling in the same country.

For a little bit of history:

https://en.wikipedia.org/wiki/Deutsches_Eck_%28transport_link

https://en.wikipedia.org/wiki/Privileged_transit_traffic