This is one of those decisions that I've changed my opinion on many times and probably will again. The chief Confederate re-enforcement I'm concerned with here is Van Dorn's army in Arkansas.
In early March Beauregard began lobbying Van Dorn to come to Corinth as part of the concentration there. Beauregard did not have the authority to command him to do it. Van Dorn hemmed about the decision until about mid March when A.S. Johnston finally ordered Van Dorn to Corinth. In the meantime Van Dorn had attacked the Union army near Pea Ridge and had lost that battle.
Van Dorn arrived after the battle but had Johnston ordered him a couple of weeks earlier Van Dorn may have made it in time. If Johnston had ordered Van Dorn's army to Corinth earlier he would have had another 15,000 men and that may have been enough to swing the battle. Of course the Union might have also been able to transfer men in time to Grant to offset Van Dorn.
While it is difficult to determine what the alternative situation would have been had Van Dorn arrived, it is clear that his arrival would have effected the battle in some respect. The overall result may have been the same but the battle would have been fought differently. The war in Arkansas in 1862 would have been much different with Van Dorn’s army out of the state.
I am reluctant though to call this a critical decision because this exercise could continue with every battle before Shiloh. For every unit that was not at Shiloh but could have been it could be asked what if they had been there. The other big group of men who missed Shiloh but might have been there were the men Floyd-Pillow-Buckner surrendered at Fort Donelson. Then we could examine the decisions they made that prevented them from escaping before Grant encircled Fort Donelson. Like I said this exercise could continue ad naseum.
If Van Dorn's troops had been engaged on the first day it seems difficult to think that they would not have made a difference, perhaps they would have been enough to win the battle before Buell's army arrived.