Firstly, the idea that Indomitable would have joined Force Z but for her grounding damage in the West Indies, is a myth.
The Admiralty had decided around Aug 1941 that no carrier would be allocated to the Far East. Had the grounding not occurred, Indomitable was due at Gibraltar around the end of Nov. At that point Ark Royal would have been released for a much needed refit scheduled to last until at least April 1942. See Boyd.
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Ark herself would have completed another “Club Run” to deliver Hurricanes to Malta prior to the end of Nov 1941 had she not been sunk. The aircraft were already at Gibraltar.
Indomitable’s Air Group included a 12 Fulmar II and 9 Sea Hurricane Ib. How effective they potentially would have been against Japanese attackers would depend on a number of factors:-
1. How early Indomitable’s radar picked up the attackers (depends on height).
2. How many fighters were already airborne on CAP and their location and height relative to both the ships of Force Z and the approaching enemy
3. How well her fighter direction team could direct any airborne CAP to those attackers
4. How many aircraft were ready for immediate launch on deck. That might depend on how likely it was considered that enemy aircraft might be met (remembering that the Japanese were operating at extreme range and had already turned for home, and beyond what the RN thought was possible).
The interception problem was complicated by there being several waves of attackers coming in at different heights.
First attack on Repulse - 8 G3M at 11,500 ft each carrying a single 250kg bomb
Second attack on Prince of Wales - torpedo attack at 200ft by 8 G4M
And so on. That makes the interception problem more complicated. This is the same problem that the Japanese faced at Midway. But at least the British aircraft had radios allowing them to be redirected while in the air.
4 months later during Operation Pedestal in the Med where 3 carriers were available with 74 fighters to begin with, the procedure was to keep a section of Sea Hurricanes at 12,000ft and a section of Fulmars at 2,000ft with more manned on deck ready for immediate take off.
But allowing for aircraft maintenance & unserviceability, and the need to maintain that CAP throughout the daylight hours, that level of air cover would have been difficult, if not impossible, for a single carrier to maintain. Any aircraft not airborne, or ready on deck would have needed refuelled and rearmed before being available for launch (aircraft not immediately needed were kept with fuel tanks empty as they were a fire hazard in the event of an attack).
Indomitable’s armament in late 1941/early 1942 was 16x4.5” (8x2), 48x2pdr (6x8) and 8x20mm (8x1).
So I’m not sure enough aircraft could have been put in the air quickly enough to have changed to overall outcome.
Edit - Even in Sept 1939 Implacable and Indefatigable were not expected to complete until late 1941 to mid-1942. After that completion dates only moved backwards for a variety of reasons. Allowing for work up time neither could have been available in the Far East in Dec 1941.