It’s hard to say how the sea battle itself would have gone if the two fleets had met. The pre-Midway Imperial Japanese Navy was still a first-rate force, and the Royal Navy had a long tradition of skillful and aggressive sea combat, so both sides would have probably made a good fight of it. ABWorsham quotes a two-to-one disparity in carriers in favour of the IJN, so this would have been a significant plus on the Japanese side. I haven’t looked up the details of each side’s dispositions, but one factor with unpredictable effects would have been whether the RN’s carriers included any of the ones they produced with heavily armoured flight decks (such as Illustrious): they had the advantage of being harder to sink but the disadvantage of carrying only about half the number of planes of an unarmoured carrier (which lessens both their offensive striking power and their defensive combat air patrol capability).
In terms of India and Ceylon, however, the capture of both of those would have required Japanese ground troops. Japan was already becoming overextended in that department at that point of the war: lack of troops was one reason why the Japanese advance ran out of steam at Guadalcanal and in New Guinea, and why Japan was never able to occupy more than strategic parts of China. Japan might have perhaps managed to capture and hold Ceylon for a while, given that it’s a fairly small island, but occupying a country as big India and with such a large population (India contributed 2.5 million troops to the Allied war effort) would have been out of the question.