I would have to disagree. I think the battle was over months before any real shots were fired thanks to American code-breakers deciphering JN-25.
Well, that was definitely a start, but there were other factors, like Nagumo's air strike against Midway base that sort of betrayed his position, or the fact that American torpedo bombers took all the attention of Japanese fighter cover (of all the crews, just one pilot survived that attack), thus allowing the dive bombers a clear shot. Anyway, back to the game.
I have written this already in another topic, and I repeat here: while I think that land battles in Civ4 are handled more or less Ok (if not in detail, the end result is usually believable), naval combat is really messed up. I remember when, first time playing Civ3, I noticed my aircraft cannot sink some stray galley, and was very sure it was a bug; I simply couldn't believe they went with the same nonesense in Civ4.
Of course, this is merely a part of a much broader picture that also has:
- battleships "intercepting" subs attacking a stack that has no destroyers;
- submarines fighting against full firepower of a battleship (artillery duel?

);
- destroyers with 3/4 firepower of a battleship (heavy cruisers, if anything);
- chance of sinking a battleship by hitting it with 20 galleons (happened to me

);
- absolutely ridicoulus "invisible" destroyers that can only be seen by other "invisible" destroyers, but for some unknown reason fail miserably in sub detection (yes, this can easily be modded out, but it's not the point);
- carriers reduced to minor support role;
Let's not get into finer points of modern naval warfare...
It almost looks as if the game makers tried (with various levels of sucess) to make land battles "realistic" (as much as the rock-paper-scissors system allowed; I still miss zones of control and stack destruction rules from civ1/2...), they totally gave up on naval warfare, and just came up with a random set of rules. Inability to sink ships with aircraft is just one of the worst cases. The argument that allowing this would make air force too powerful doesn't mean anything IMO, as IRL this is exactly the case - undertaking any sort of major military action under conditions of opponent's air superiority is suicide. It was the case since WWII and it probably stays that way in forseeable future.
IMO the reason for this is that the game makers wanted to avoid extra complications that would have arisen from creating an entirely separate ruleset governing naval combat. Stretching rules for land battles to naval warfare led to oversimplification and situation where "bigger stack always wins" (heh, they even didn't bother with extending the "rock-paper-scissors" system byond ship of the line vs frigate situation). It's worth noting that in vanilla/warlords air forces also seemed to recieve no love at all, aircraft were not even "real" units back then ("real" as in getting promotions/experience). It seems that initially naval/air combat was intended merely as a addition to land warfare.