Axis carriers could cause panic without being good ships

Would operational German or Italian carriers have mattered even if their designs were poor?

Yes; their existence alone could provoke disproportionate Allied caution and political pressure for matching Axis carrier programs.

Even a weak Axis carrier would force the Allies to plan around it. Graf Zeppelin and Aquila did not need to win a carrier battle to distort deployments and provoke caution. Both designs look particularly poor because Germany and Italy could observe the much more mature carrier practice of their Japanese ally. If Germany commissioned Graf Zeppelin, Mussolini's prestige concerns would probably accelerate Aquila regardless of whether her systems were ready.