I suspect that the lessons from Wake etc were the reason why Yamamoto changed up the Midway fleet composition. Their biggest battleships and numerous cruisers, including the 18" Yamato reserved for just that effort. More than one bombarding taskforce specifically prepared and assigned.

I think we might be under-estimating the contributions of unchallenge air superiority and big gun battleship shore bombardment support as we eventually succeeded with. MacArthur wrote 'no-one prepares fortified defenses as well as the ****' and yet with old battleships and cruisers and carrier support the USN would succeed in the same endeavours.

With continual carrier-born air attacks(especially on that kind of terrain) and cruiser even Yamato 18" battleship bombardment, (and no bunker we had there would survive those), they could change the odds drastically.

I've read Spruance, Nimitz and Fletcher and none of them mention confidence in holding Midway if the US carriers didn't succeed the way they did. But of course that's the Navy for you .

With no replacing supplies or reinforcements, Midway defenders would be faced with the same problem as Iwo Jima. It wasn't an island like Hawaii after-all, it was pretty much the ideal set-up for Yamato, Nagato and Kirishima let alone cruiser bombardment till surrender. The Americans were not likely to fight to the death like Iwo Jima. Especially if they heard the carriers were sunk, routed or not coming to their rescue like Corregidor.

According to books on Midway, despite reinforcements, the supply situation was dire. It really wasn't a very big island with very many buildings or bunkers to stockpile and store safe from bombardment. It's a surprisingly small, accessible from every angle all over, wide open vulnerable terrain to defend. Ideal for attackers, a bugger for defenders.

So from what I've read, yeah, the Japanese would conquer the Island if they won they won the carrier battle or the US fleet wasn't there anymore for whatever reason. Yup, I think they'd take the Atol.