These are memories after the fact. Contemporary primary sources show:
1) Sherman's insistence that Grant's cooperation was expected was fabricated after the fact to cover his embarassment, much like his insistence that he had withdrawn just in time to avoid a flood that covered the ground he had just held in 40 feet of water (heh). Prior to the assault, Sherman expressed the plan to his brother John: "[Grant] will move south as soon as I am in position at Vicksburg." In other words, any movement by Grant was wholly contingent on success by Sherman.
2) Grant showed no urgency trying to inform Sherman that he was withdrawing to Memphis. In fact, until Grant heard from Sherman directly, and for a time shortly afterwards, Grant was convinced that Vicksburg had fallen. If Grant had sent a courier to Memphis on the 20th, and from Memphis by steamer to Sherman, he could have gotten word to Sherman before the assault on the 29th.
3) Sherman understood the importance of establishing a foothold on the Yazoo bluffs, and had expressed several times that this was the key to taking Vicksburg. Prior to Sherman's return to Memphis to lead the riverine operation, Sherman wrote "if you have reason to believe Steele has taken Grenada a force of 10,000 men ought immediately to go by river to mouth of Yazoo and occupy the land back of Vicksburg between the Yazoo and [Big] Black River." Why would Sherman have reservations establishing a foothold on the Yazoo bluffs with 30,000 men when he expressed no reservations doing the same with 10,000 men? In both instances, Pemberton would be free to turn against this position with his whole force.
Grant expresses in his memoirs that Van Dorn's raid prompted him to return to Memphis. This much is true, but Grant would have returned to Memphis regardless of Van Dorn's raid ... to have done otherwise would have seen McClernand moving on Little Rock with the bulk of Grant's army. Would you really like to argue that Grant, with direct orders not to proceed with an overland campaign, Sherman, McPherson, and Porter pushing him to take command of the riverine operation, Lincoln himself insisting that the riverine operation be made the primary focus of his department, and McClernand taking the bulk of Grant's army off on a "wild goose chase" that Grant would not have moved back to Memphis to take command of the riverine operation?
I say the great irony of Van Dorn's raid is that it expedited by several weeks Grant's arrival at Milliken's Bend and the eventual fall of Vicksburg.