A battered French fleet still completes its convoy mission

Did the French convoy reach Messina after Stromboli?

Yes. Duquesne took the convoy around Sicily and delivered it to Messina without another battle.

The French convoy reached Messina despite the damage to its escort. The Dutch ship Essen sank the following day, while no French warship was lost. Duquesne received eight additional ships from Messina, then avoided another action when the Spanish squadron appeared and the combined opposition had superior numbers. He took the convoy around Sicily and brought it into harbor without further fighting. The allies went to Milazzo and Palermo for repairs, while France had achieved the convoy mission that prompted the battle.