It depends if they are aware of the error fare? It makes a big difference if you found a fare that is still reasonably priced, or something like first class around the world for $800.
If the fare is still reasonable you may be lucky and there are chances that they will honor it (and/or not even notice). But with these kind of fares nothing is for sure. I have heard stories (not Alitalia) where the pax was denied boarding at the gate due to it being an error fare.