Well, in the end, the Graf Zeppelin had different design constraints placed on her by the Kriegsmarine and the Nazi leadership. Those design constraints, for her perceived mission, weakened her airwing size considerably, and presnted some very difficult handling issues for the aircraft she would have carried in terms of both deck and hangar handling.
They also added an offensive gun armament that was unnecessary because it weakend her principle armament, her airwing. if faced with so much as a heavy cruiser on the surface, she would have been vastly under gunned.
She was stronger in terms of her overall structure, and this would have been good for the Arctic Ocean and North Atlantic. Fact is, she was not meant for the fleet type engagements that the US and Japanese carriers were designed for, and which they anticipated.
Still, with 12 or more Me-109s for air cover she could have fended off small scale torpedo and bomber attacks. A pressed attack however, by a large number of torpedo bombers and/or dive bombers, particularly if escorted by a good group of fighters from an adversary carrier, would have surely overwhelmed the Me-109 contingent.
With 30 Ju-87 Stuka dive bombers, she would have had an effectiv strike force. However, once again, her adversaries were going to haver that many dive bombers and that many torpedo bombers again to attack her. She needed a group of torpedo bombers as well, to be able to come in on the deck with, while dive bombers came in high against adversaries.
This shows all the more (IMHO) that the Germans meant her to raid, and to excort raiders and give them an added layer of protection...which as it turned out, they desperately needed.
If the Graf Zeppelin had been able to get to the shipping lanes with a couple of battleships and heavy cruisers, and with a screen of destroyers, it would have been a MAJOR problem for the allies.
But she never did (as the history below indicates). We are all speculating about what may or may not have happened, and about her known characteristics and how they may or may not have worked out. It is an interesting discussion.