Halleck had already ordered Grant not to continue any farther south overland. Grant had plans to join Sherman when Sherman made a lodgement on the Yazoo Bluffs and could supply him via the Yazoo. But Sherman did not make that lodgement. Of the force that stopped Sherman in his tracks, none of the brigades that saw combat were from Grenada. Of the two Grenada brigades that were at Chickasaw Bayou, one skirmished with the federals across an unfordable body of water, the other sat in reserve. Both brigades had been ordered south before Pemberton was aware that Grant was retreating to Memphis.

So without Van Dorn's raid, Sherman is still stopped cold. McClernand arrives and assumes command, taking the army off to reduce Arkansas Post and then contemplating a movement against Little Rock. Grant learns that McClernand is about to take the bulk of his army off into the Trans-Mississippi, and travels to Arkansas Post to assume command after leaving orders for his men to withdraw to Memphis.

If anything, Van Dorn's raid expedited by a couple of weeks the event that would eventually see the fall of Vicksburg: Grant moving with his entire force to Milliken's Bend and assuming command from McClernand.