Personally I haven't made use of these facilities, but friends of mine from Hamburg have taken the "Autozug" to Munich and to Narbonne for the same reason as you're thinking of. Plus that you arrive in the south totally relaxed.
In your case I'd suggest to take the train to Munich or Innsbruck/AT. The Munich-East station is situated quite near the motorway leading out of town to Salzburg. Once outside Munich you could take the secondary roads through the beautiful bavarian countryside into Austria.
Only when we pause to wonder
do we go beyond the limits of our little lives.