Too bad Sommerville's three carriers at Ceylon weren't equipped with folding Martlets instead of Fulmars and Sea Hurricanes. Not possible I know.
Formidable had brought 888 squadron with the folding wing Martlet II with her from the U.K. Nominal strength 12 aircraft. There was supposed to have been 6 serviceable during Operation C. IIRC another 3 had been left ashore at China Bay for pilot training.
I'm not 100% but I'm pretty sure the answer is negative. The FAA sent Hellcats and Corsairs to the Pacific and kept the Martlets in Europe. I'd be delighted to be proved wrong...but I'm confident my info is correct.
While I'm not aware of any combat between RN Martlet/Wildcats and the IJNAF/IJAAF other than already noted, they were used quite a bit In the Indian Ocean area.
So in 1942 Formidable was the first to use them until she left for home in Aug 1942, followed by Illustrious until she left for home in Jan 1943. Also Indomitable had a few from May-July 1942 before she left for the Med and Operation Pedestal.
During 1944 a number of RN escort carriers operated in the Indian Ocean and Bay of Bengal on anti submarine patrols with Wildcat fighter flights attached to their Swordfish / Avenger squadrons. Battler (834 squadron where Wildcat V replaced Seafires 6-10/44), Shah (851 squadron 4/44-2/45), Begum (832 squadron 1-11/44), Ameer (845 squadron 2/44-2/45).
Also in 1944 Atheling operated briefly as a fighter carrier in the Indian Ocean with 889 squadron with Seafires and 890 with Wildcat V May-July 1944.
And finally HMS Searcher took 882 squadron with Wildcat VI to the IO in the summer of 1945 in time to participate in Operation Zipper, the re-occupation of Malaya in Sept 1945.
And let's not forget Victorious in the South Pacific in summer 1943. But again no action against Japanese aircraft.