Politics would've killed it long before then. The Italian airforce stonewalled virtually every attempt by the Navy to get into the fixed-wing aircraft business and as they had far more weight with the Fascist party they got there wayIn immediate post Great War Italy, the conversion of Leonardo da Vinci's damaged hull into a carrier was considered. The Italians decided the hulk was too damaged for such a conversion. The Navy had also considered a new build fora carrier. Perhaps during this time of financial strain, the Italians are able to acquire the final design for Hermes, with the British concerns over her size and weaknesses. The Italians review the design in the mid to late 1920's, increasing the size of the ship by 30-40%. In 1929, the Italians order a new Leonardo da Vinci in the form of a CVL. Do they have time to develop viable carrier doctrine before stumbling into the next Great War?
The enemy always gets a vote and the Brits could and would out-build the KM several times over. Any attempt to try and hit the RN anchorages at Scapa and Rosyth is liable to intercepted both by British land-based air as well as by the RN's own carriers and it's not like the Brits wouldn't assign a carrier or two to cover their own capital ships if they know the Germans have a carrier of there own.My vote is the Graf Zeppelin, just not as she was conceived or built. The first task of the KM is to counter the RN, to in a nutshell Pearl Harbor her battle line, and she had one or two ways to accomplish the task. More ideally the navy would gain a long range heavy bomber that could sink battleships at anchor, add long ranged torpedo bombers to in fact pull off a Taranto or PH, and the KM opens the door to the Atlantic. Oddly the former might suggest the He177 dive bombing strategic bomber, a plane that can hit a pin point target, but we digress into odd corners. Next best is to take the aircraft to the British anchorages. So despite my best efforts to find fault with a carrier for Germany, I can see a mission, and that mission demands something not aimed at lone distance hunting of merchants, not designed to be a raider, but rather a ship that can move a strike group to position, support it, and launch a raid to sink the Battleships before they get to sea, to strike one blow to level the playing field. I offer no promises it works, but that is the mission, the Graf Zeppelin would not be the bodge it was, rather a true strike carrier. I promise nothing as to if Germany can design or build this ship or her sisters, no promises on the aircraft, but if you want a fantasy ship, that is the carrier the KM could use to its war upon the RN. So if my KM Admirals cannot get warm and fuzzy over chasing commerse, then here is a real war making ship for their consideration.