One thing worth noting on this is the effect this might have on non-fighter aircraft. The US Navy could have certainly put a couple more PBY into the air along with the USAAF possibly getting some bombers or other search aircraft up. These would present a real threat to the Japanese fleet if they found their location.
This alone might have even caused Nagumo, who certainly seems to have been cautious in his actions, to cancel a second strike electing instead to retire after recovery of the first one.

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Truth is stranger than bullshit!