I think it that asking a defeated Italian Army keep fighting against the former allies at that point would amount to ask them to mutiny and make a revolution. And I can definitely see them doing that, with lots of people left and right competing to lead it. No one would have the stomach to keep fighting anyone after a defeat to the Austrians so severe that it calls for peace.
Also, the strategic benefit of the switch would be questionable at best. The Entente would be in the position to swiftly take over Italian colonies, and probably stop any Italian move on the Western Alps (which are an even worse terrain for WWI-style warfare than the Eastern Alps the Italian army had bled itself white over earlier) especially since any such move is bound to be extremely chaotic.
Britain can easily starve Italy for coal and even food, and 1917 Germany is not really in the position to help very much. If Italy doesn't just collapse internally simply because of the popular reaction to such a clearly stupid move, it may be defeated militarily... again (and then likely collapse internally).
Italy on the CP side would be extremely helpful to them... but not a battered 1917 Italy switching sides. The US are already in the war, so it is hard to think that this switches the balance to CP victory IMHO.