They will not load your bags if you do not make the flight. For international flights, bags have to match passengers so if a passenger checks in bags but does not board the flight, the bags have to be removed from the flight.

On AA, the gate agent will radio down to the ramp to let them know which standby pax have been cleared and who's bags they can load. Other airlines probably do something similar. In your situation, I would try to carry on if possible. If your bags are tagged for FCO but you end up making the MXP flight, there is no guarantee that the bags will be rerouted to the MXP flight. You may have to gate check anyway but will be limited to the 3 oz/1 quart bag per passenger limit.