What would happen if the Italians accepted Austria's offer of Venizia, in exchange for not entering the Austro-Prussian war.
With freed up troops how would Austria fare in the war?
Could Austria win? would they unify Germany, or just Southern Germany?
Could a Catholic non Austrian Southern Germany Emerge?
Would there be a Franco-Prussian War?
If not would Rome ever join Italy?
Would there be a WWI?
What places would be the targets of future Italian Irrendism ?
If they did then they would be appeased for the moment; however, Prussia is so much more proven on the battlefield than Austria is (of the two dominant German states, Prussia has the powerful army while Austria has the good navy), and it must be noted that Russia had to help Austria against the Hungarians in 1848 while Prussia were the reactionary police themselves.
So, while this may free up Austrian resources Prussia is still going to give them a hell of a time; at the least the war's up in the air.
The Franco-Prussian War would still happen if Napoleon III is still a diplomatic dupe and tries to play its hand in the Luxembourg Crisis and the candidacy of Leopold of Hohenzollern on the Spanish throne. And obviously Italy will want Rome as a capital; remember Europe's obsession with the Greco-Roman civilization that was only blunted by the Second World War.
And Italy will still want the Tyrol and Istria/Dalmatia, the former due to the Italian speakers in the area and to serve as a more defensible border, while the latter has a historic importance to Italy (hey, if they have Venetia, why not go after the lands of the Republic of Venice too?) and also has some Italian speakers. Getting back Nice, and to a lesser extent, Savoy, will matter too for more radical irredentists - Garibaldi himself was angered at Cavour's horsetrading of his hometown to France.