Travel to Dachau would be covered by the Bayern-Ticket, but it would cost more. Why pay more if you don't have to? A Bayern-Ticket costs €27 online or from a ticket automat, €29 for personal assistance at a ticket counter, and it is valid all day for up to five people. A Muenchen XXL Partner Tageskarte is valid for all day travel in the inner two zones of Munich MVV for up to five people. It costs only €11,80. You can buy one from any ticket automat in Munich or, for the same price, from a ticket counter. Both the Bayern-Ticket and the MVV XXL Tageskarte cover the S-Bahn to Dachau and the bus to the memorial.
With a Bayern-Ticket, on weekday, you can only travel after 9 AM; the XXL Tageskarte is valid anytime.
Trains of all classes, express and regional, as well as S-Bahns use that line through Dachau, although the express trains do not stop there. There are regional train that stop at Dachau, but they only originate at the Hbf. You can't take a regional train from Marienplatz to Dachau, but you can take the S-Bahn from Marienplatz.
Are you going on to Rothenburg the same day as Dachau, or are you going back to Munich for the night and then going to Rothenburg the next day. If you are doing it all, Munich to Dachau to Rothenburg, on the same day, then a Bayern ticket would cover all of your travel.