the Department of State website says Austria is a Schengen country so it would be a Schengen (VIE) to Schengen (HAM) connection.
I guess what I am looking for is for anyone who has traveled through VIE and done this type of connection when starting in the US. My international travel experience is very limited so before I even consider booking this, I wanted to get feedback. The offerings for miles this summer are extremely limited (I dropped to Gold this year FWIW) so I want to hop on this if it is even remotely possible to pull this off.