German Train Pass

Yes. Because Salzburg is a border city, any pass that includes Germany will be fine.

Another option: save your railpass day and travel on a Bayern Ticket, a daypass for the regional trains. A railpass day costs about $40 each. With the Bayern ticket you pay 29 Euros for a group of 2-5 people. It's a 2-hour direct trip on the RE train, which leaves every hour or so.

Thanks so much for the update.

For one person, the Bayern-Ticket Single is €21. On workdays, the Bayern-Ticket is only valid for travel after 9 AM. The first regional train after 9 leaves Munich Hbf at 9:42 and gets to Salzburg at 11:42. There is an earlier train that gets to Salzburg at 10:42, but it leaves Munich Hbf at 8:48, when the Bayern-Ticket is not yet valid. However, if you buy a Bayern-Ticket AND a local MVV 3 zone ticket to Grafing Bahnhof at €7,50 pP, you can leave on the 8:48 train. The train gets to Grafing Bahnhof at 9:11. You don't have to get off the train there, just show the conductor the Bayern-Ticket after Grafing.

does this bayern ticket also work going from Salzburg to Munich? for a family of 3

Yes. It's valid for anywhere in Bavaria, and that includes into (or out of) some border stations just outside of Bavaria. In addition to Salzburg it is valid to Kufstein, Austria, on the Inn going to Innsbruck and to Ulm, which is just across the border in Baden-Württemberg. It is also valid for travel between Memmingen and Lindau on a loop of track through Kißlegg and from Kempten to Garmisch-Partenkirchen via the Ausserfernbahn in the Tirol. Here is the entire track plan for Bavaria. The Bayern-Ticket is valid for all modes of transport (S-/U-Bahn, trams, and buses) in the transit districts, like Munich and Nürnberg. The German Rail and Eurail tickets are only valid for the S-Bahn in these cities. I don't see anything on the German Rail Pass web page or the Eurail website to indicate that those passes include the Ausserfernbahn or Kufstein.