I doubt that the British would allow the Italians to import unlimited amounts of oil and raw materials to pass on to the Germans: they’d know how much Italy needed for itself, and would only let them have that much, with a small surplus to allow for growth.
This hits it squarely. Even in early 1940 the blockade was taking effect with a neutral Italy, and Norway, Sweden, Greece, Yugoslavia, Rumania, Truky, & USSR. One of the rational Mussolini used for his DoW on France and Britain inJune 1940 was the negative economic effects of the import quotas or restrictions Britain assigned to neutrals, and its enforcement. Even that early the NavCerts system, was working well enough to take notice, and Anglo/French warships inspecting violators they ran down were picking off contraband cargos.
So yes the Italians can make profits selling Germany war critical resources, but no, neither they nor the other neutrals are a wide open conduit. And, the conduit constricts as Britan becomes more efficient at running the blockade of Europe and accquires the full assistance of the US 1940-41.