An Einfach-Raus ticket is only good in Austria. The fastest, most normally used route to Salzburg goes from Hall to Kufstein, Austria, then through Germany to Salzburg via Rosenheim. The only Austrian trains that can use that route through Germany are the express trains. They go non-stop through Germany. The Einfach-Raus ticket cannot be used on these trains, but you could buy an Austrian Rail ticket all the way. The RailJets do not stop in Hall; you would have to take an S-Bahn from Hall to Jenbach and catch the RailJet there. I'm sure an ÖBB ticket purchased in Hall would include the S-Bahn to Jenbach.
If you want to take that route, but avoid the more expensive express trains, you can take the S-Bahn from Hall to Kufsteins and use regional German trains (Meridian) from there to Salzburg. For the part from Kufstein, which is a border station for German Rail, to Salzburg, you can use a Guten-Tag-Ticket, which is like a Bayern-Ticket except only good on Meridian trains, which are the regional trains from Munich to Salzburg via Rosenheim and for Kufstein to Rosenheim. The Guten-Tag-Ticket cost 23€ for the first person, 6 each for person 2 to 5.
If you take the S-Bahn from Hall to Kufstein note that you must purchase your ticket in advance at the station and validate it. You cannot buy a ticket on the S-Bahn and you will be fined if you don't have one.
Another alternative using the Einfach Raus would be to use regional ÖBB trains to Salzburg via Bischofshofen. That route would be slower by several hours (it's longer because it goes around Berchtesgaden to the SE). It has a change of trains in Zell am See or thereabouts.
Except for the express train ticket including the RailJet, all of these tickets can be purchased at the time at the station. There would be no discount for advance purchase.
Looking at Trainline, they, of course, don't show any of the fares using regional passes (Guten-Tag-Ticket or Einfach-Raus-Ticket). They do show the connection using an Austrian express train through German. That's the most expenive ticket they sell at 59,-€/P. They do show a connection using the S-Bahn to Jenbach, an EC from Jenbach to Rosenheim, and a Railjet from Rosenheim to Salzburg. That connection is 19,90€/P, which is less than any connection except the Einfach-Raus-Ticket for the trains via Bischofsheim.
