Would a larger Taranto raid free Italy's cruisers to fight?

Would Italy's cruisers become more active with fuel freed by battleship losses in a four-carrier Taranto raid?

Possibly, but the raid could destroy heavy cruisers too, and surviving cruisers would still struggle to attack convoys guarded by British battleships.

Destroying Italian battleships could leave more fuel for surviving cruisers to operate. A raid of around 120 aircraft from four carriers could also hit the three heavy cruisers in harbor, combining damage comparable to Taranto and Cape Matapan in one attack. Surviving cruisers could sortie more often, but even a slow British R-class battleship could keep them away from a convoy with its 15-inch guns. It would not need to catch the cruisers to prevent their 8-inch batteries reaching the protected ships. A later suggestion is that four carriers' fighters could cover British battleships waiting to intercept escaping Italian ships, allowing a later withdrawal and more operational risk. In the larger counterfactual, Italian fleet losses might cut reinforcement routes to North Africa and help Britain retain Crete. Reduced Mediterranean commitments could then free Queen Elizabeth-class battleships and carriers for the Indian Ocean, creating an earlier deterrent to Japan. The possible political shock to Mussolini depends on this chain of military setbacks.