Not if they kept changing it or upgraded it.
If Midway is occupied the Japanese naval range increases whilst the American naval range decreases. I'm not saying the Japanese would threathen Hawaii directly from midway, they would just be able to use Midway as a staging area for any sorts of things.
Besides, if Midway goes well the attack on Alaska goes well too and the Americans have a lot more problems to rid themselves of than just the threat on Hawaii. Meanwhile Japan goes all out on the Solomons and further south, making things ever more difficult for America and its allies(like Australia).
Not actually sure how long the Japanese can keep the offensive up though. Their planes, men and ships were already worn out. They have to stop at some point and catch their breath, but they might feel like they can't afford it(which is true). Instead of owning it they always seem to be catching up to the momentum.
It has been argued out on these forums before that the Japanese simply did not have the doctrine or equipment to take Midway away from the garrison it had at the time of the battle, and that the IJN was 'very wary' of getting close enough to serious coast defences to do a proper job of softening up before landings.
Second if the Japanese actually DO take Midway, they have to hold the blasted place. Taking it means supplying the garrison, with a string of American held island leading to a major American naval base. Submarines from the base will be preying on the supply ships, while airbases can be built on islands closer to Midway so that it - and the freighters that were already in short supply - can be attacked.
The comparison made might be with Guadalcanal, with USN forces attacking Midway in place of Japanese forces coming 'down the slot' from Rabaul. A long slow grinding battle of attrition follows in both cases, with the US production capacity - of equipment and properly trained crews - meaning the Japanese can't win, can't break even and can't get out of the game (except by abandoning Midway). Abandoning Midway would of course be a public admission of defeat and a very hard thing for Japanese officers and politicians to face.
Would there be the resources left to do Guadalcanal and the other things that happened OTL mid-1942 to late 1943?
Or would the struggle for Midway soak up all the available ships, planes, and men?