Would that be any different from OTL?
After Koniggratz the Austrians pulled South Army from Italy to hold the line of the Danube. The Italians of course overran Venetia but when they tried to push beyond that were held by local forces. So no change is likely there even if Koniggratz is a bigger Prussian win than OTL.
The armistice between Austria and Italy was signed in Cormons (Friuli) on August 12, 1866. The armistice between Austria and Prussia had been signed three weeks earlier, on July 21.
At the time of the armistice of Cormons, the main Italian army under gen. Cialdini had taken Udine, the fortresses of the Quadrilateral were being invested by another Italian army under gen. Cadorna and Garibaldi,commanding mainly volunteer forces, had broken the Austrian resistance in Trentino and was ready to enter the city of Trento.
It looks like that only a portion of the Southern Austrian army had been pulled from the Italian front (the fortresses were still manned, and the defense of Trentino was by regular jaeger regiments, not just "local forces") and anyway there was no more need to keep the southern army on the Danube, since the armistice of Nikolsburg had been signed and the Bohemian theater had been quiet for three weeks (effectively Prussia and Austria had already negotiated the main terms of the peace of Prague, which was signed on August 23, just 11 days after the armistice of Cormons). Italy had been fighting alone Austria since July 21 and had been under strong pressure from France to terminate hostilities. Was caving in and signing the armistice the right thing? Probably it was, given Italian diplomatic isolation and French pressure. Certainly it did not came to be because they were stopped by "local forces"
iven that Trentino and Trieste are both part of the traditional "Reich", Italy can expect no Prussian support for such moves.
Which "traditional Reich"? The traditional Reich (HREGN) had been formally dissolved in 1805, by which time it was neither traditional nor a Reich. Bismarck (who in the end managed always to have his way) had already managed to convince the king of Prussia that marching on Vienna after Koniggratz was not a viable idea and had already decided that any serious punishment of Austria was not in the interest of Prussia (not "Germany": Prussia). He would not have supported Italian claims beyond Veneto and western Friuli because of his long term strategy to keep the Austrian state viable as a future ally, but certainly did not give a fig for romantic notions of the traditional territories of a non-existing Reich