It takes a couple weeks for Op ANTON to be completed. Most of the unoccupied Zone is swiftly overrun, but some enclaves hold out. Notably the fortifications surrounding Marseilles & Toulon.
But, its still a game changer. In Tunisia the garrison commanders @ Bisect & Tunis receive unequivocal orders to resist the Germans. A major airborne operation must be mounted to seize a port. The week delay in organizing that allows Allied reinforcements to reach the cities & any Axis enclave is confined to a few kilometers radius around one or the other city. By December Allied air groups are installed on the all weather airfields of Tunisia. From there they can interdict Axis efforts to sustain or evacuate the residual army in Lybia. In the end the Axis lose a quarter or maybe half of what they lost in manpower in the early months of 1943.
The rainy season will interfere, but Allied air superiority will allow opening the Sicilian straits to convoys months earlier than June 1943.
At the SYMBOL Conference in January Eisenhower tells the Joint Chiefs 'Mission Accomplished' and the latter set to arguing about the next move some time in March.