I would consider that it is possible (tho a long shot) that Italy could have been driven out of the Great War after Caporetto. There is a very good book looking at just this particular battle Mario Morselli's Caporetto, 1917: victory or defeat? If the Germans and Austrians had really worked closely with each other - and particularly certain Austrian officers working better with each other - a greater portion of the Italian army could have been cut off and captured.
The Allied troops were not to get involved if there were a general collapse of the Italian army. The Italian people were not entirely behind entering the war until the shock of defeat at Caporetto with a defeat greatly magnified they may turn on Orlando and seek a cease fire.
I frankly doubt that the CPs could have gotten more than they did out of Caporetto (which again it was a dumb idea to start with and would not have been decisive in any case): they pushed the front back to the Piave and captured more than 250,000 prisoners, not to mention a lot of artillery pieces.
It is just not reasonable to postulate that they could get more.
BTW, it would have been also impossible to manage a better coordination in the attack, considering the length of the front: by comparison you should look at the botch up they made with the attack of 22 June 1918 (and which lasted one day). It's also to be noted that there was quite poor coordination on the Italian side: the relations between Cadorna and Capello were less than friendly.
As far as the politics of the post-Caporetto, there was never any doubt that Italy would have stayed in the war. The king moved to Peschiera to stay closer to the front, and all the parties in parliament supported war continuation. The only exception was to be found in the left faction of the socialist party, but their influence was minimal. When the continuation of the war was discussed in parliament it was approved by acclamation.
You're right when you say the Allies were not ready to commit troops to the defense of the Italian front: during the meeting in Rapallo the French in particular were very cold and the discussions were not really positive. It took a second meeting in Peschiera, with the attendance of the king, to thaw a bit the situation. However even after Peschiera the allied troops allocated to the Italian front (10 divisions from France and 4 from UK) were not positioned on the front but were kept as a reserve. Ultimately the front after Caporetto (as well as before) was held by the Italians only.