For the first two years of the war, the majority of fighters fielded by the Fleet Air Arm were Blackburn Skuas, Gloster Sea Gladiators and later on Fairey Fulmars. The Martlet didn't get to sea with the Royal Navy until March 1942 when six were embarked on HMS Illustrious. Main problem seems to have been that these aircraft had originally been intended for the French Navy and lacked folding wings. The Hawker Sea Hurricane first went to sea in July 1941. Seafires made their combat debut in November 1942.
As for the Bf109T, in terms of pure performance it was roughly comparable with a 109E (which it was derived from), and so would have been superior to Sea Hurricanes and Martlets. It would undoubtedly have had an extremely low servicability rate, coupled with an astronomical accident rate. It would have been extremely challenging to try to operate aircraft with that undercarriage and that canopy from pitching decks.
However, I am not arguing for the 109T. I am suggesting that a sane and pragmatic leadership would have been less ambitious in the design and expectations of their first aircraft carrier. Given that the Graf Zeppelin was laid down in 1936, I will stick my neck out and suggest it would have been possible for a 16000 ton commerce raider carrier based on the Deutschland class hull to have been laid down in 1935 (using a smaller existing hull would have shortened the design process and made it much easier to find a slipway to build this thing), launched in 1937, and then commissioned in 1939 or 1940 with an air group consisting of Arado 197s and Fieseler 167s. I can then see it undertaking commerce cruises like Admiral Sheer, Graf Spee and the twins.
Wouldn't have affected the course of the war, and probably wouldn't have achieved too much, but would have been a far more reasonable option to fulfill Ovaron's dream of an operational German carrier.