No, but it would try to increase its influence in the easiest way possible, which would probably mean increase its influence among the German nations*. That is basicly what Prussia did, using nationalistic feelings to increase its own power. Austria probably would try to do the same (although I think that without Italy and Hungary they are weaker than Prussia and so probably less succesful).Just off the top of my head, if Austria were to lose too much of its empire, would it ever consider uniting Germany under an Austrian banner to compensate?
*or states or countries or whatever, I always get those confused