As it says on the tin. Rosecrans OTL delayed his advance almost unreasonably long as it was. What if he took another month to be ready? Would it make any difference to the Confederate situation for him to advance in late July instead of late June?
I suppose it depends on how quickly Rosecrans is sacked because if Washington is slow to act then they might just shift Grant over. I think Thomas is the senior corps commander, so he makes sense if Washington acts quickly.
Although Rosecrans may not impart his plan which worked so successfully to Thomas/Grant, the Confederates are in enough disarray already to weaken their position.