"Conceived and developed by Combined Fleet staff officers during March, 1942, the Midway Operation was the child of expediency."
The above from a book, "Hawaii Under the Rising Sun" by John J Stephan. In other words the Midway attack was planned well before the Doolittle Raid. In fact Yamamoto ordered planning for the invasion of Hawaii to begin on December 8, 1941. The Midway operation was part of that plan.
Originally an invasion of Hawaii was considered by the Japanese planners to be part of the December 7, 1941, attack on Pearl Harbor. Yamamoto decided that the invasion was too risky and canceled the planning for that. However, an invasion of Hawaii was always an operation that he thought necessary and he realised after Pearl Harbor, because of the weakness of the US defense, that the invasion would have probably succeeded. His reasoning about the invasion of Hawaii was that Japan could never win a long drawn out war with the US and that the invasion and occupation of Hawaii would give Japan a bargaining tool for a negotiated peace with the US before the US could bring her massive power to bear. Many in Japan disagreed with Yamamoto.
The Hawaii invasion plan was labeled "Eastern Operation" and it was scheduled for October, 1942. The Japanese Army was not on board with "Eastern Operation" initially but Yamamto and the Combined Fleet staff went forward with the "Midway Operation."
"To circumvent army opposition, this operation would be carried out without infantry or armor. To win support from the Navy General Staff, the operation was designed to lure the US Pacific Fleet into a "decisive battle" at a point where the Imperial Navy could use land based as well as carrier planes against it. It was called "Midway Operation."
In effect, the Midway Operation was the prelude for the Hawaii invasion. The Combined Fleet approved the plan on April 5. The Doolittle Raid took place on April 18. So that raid did not cause the Midway Operation to go forward as it was already planned and in the process of being readied. What the Doolittle raid may have accomplished was that after the raid, the Japanese Army changed it's stance and became supporters of "Eastern Operation" the invasion of Hawaii.
It boggles my mind to reflect on what would have been the outcome if Japan had gone forward with the plan to make the invasion of Hawaii a part of the Pearl Harbor attack on December 7. Given the state of preparedness of the US forces on that day, it seems that the invasion would have probably succeeded. The two carriers the US had in the vicinity would have intervened and probably have been sunk, along with many of their escorts. Of course the Japanese operations elsewhere would have had to have been altered and whether or not they could have solved the logistical problems of a prolonged occupation of Hawaii would be in question. Hawaii had about 400000 inhabitants at that time with 160000 of those people being native born or first generation Japanese.