Wild What If
Changing as little as possible, then Grant's army is on the banks of the river with the Army of the Cumberland coming up across the river from Grant and other reinforcements available soon. Then even a dispondent Grant would have had to have a round-robin discussion with Buckner, Halleck and Lincoln. Halleck, of course, would accept retreat as advisable, but Lincoln might not. In any case the retreat would be slow, Halleck would be as slow in a retreat as in advancing and for the same reason, marching only a few miles a day, before entrenching up to the eyes, for the night.
Beauregard, with his depleted, disorganized and exhausted army, would be glad to see Halleck go.
Later from wherevey Halleck retreated to, Halleck would advance with a ponderous army, at a glacial pace to Corinth (Probably).
Beauregard would probably have withdrawn to Corinth leaving a covering force at Shiloh, with the intent to later retake Fts' Donelson and Hentry. But Lincoln would be urging Halleck to resume the offensive with a army larger than the one defeated at Shiloh and Halleck was no McClellan, actively sabotaging the Administrations war effort, just slow and caution, but when he had overpowering force Halleck could be induced to advance. So Beauregard would likely retreat before such an advance.
As noted by others the absence of Grant would only have delayed the Anaconda's coils, not eliminated them.
Bringing the