Longstreet's proposal was to take his Corps and the units that made up the Army of Relief join Bragg, and suggested that Johnston take command of the whole force. If Longstreet brings only McLaws' and Hood's Divisions, he adds 14,512 officers and men into Bragg's army of around 50,000 troops to attack Rosecrans' 80,000 troops. Longstreet’s proposal is sound on paper, but logistics makes execution difficult.
Historian Thomas Connelly observed that "Bragg's own transportation system had been on the verge of collapse since early 1863." IOTL after Chickamauga Longstreet complained to Bragg that his staff officers had not been provided with the means of supplying his troops. Unless the army's wagon train could be greatly expanded then the Army of Tennessee could not venture more than a few miles away from a secure rail-head. A logistical build up that would take more than a month is needed before the Army of Tennessee+ is ready to strike a blow.
Still, Longstreet’s arrival would certainly tip the balance of power in favor of Bragg in the Tullahoma Campaign. I think Rosecrans would have waited for Grant to return the IX Corps to Burnside for the invasion of East Tennessee. IOTL the Tullahoma Campaign could have been a close run affair had it not been for the squabbling of high command and the lack of troops to really secure the gaps. If Longstreet’s command stalled Rosecrans at the gaps, Bragg might have been able to convince Polk to launch a sweeping counterattack on the Federal right. Of course, this is the Army of Tennessee - such coordination is quite unlikely.
In the East, Lee might be in trouble. While the Army of the Potomac was bleeding from expiring 9-months and 2-years enlistment, Lee’s II and III Corps had been severely damaged. The Pennsylvania Campaign, though quite costly for Lee, ensured his army would survive into the next year. More than 45 miles of quartermaster and subsistence trains filled with impressed stores escaped Pennsylvania and Maryland along with 20,000 horses and mules seized and large herds of livestock. Throughout the rest of the summer Lee's men had enough meat, flour and fodder. All of which were unavailable in Virginia. Hence, I suspect that there would be a Pennsylvania Campaign. Lee saw that the Army of the Potomac was at its weakest numerically and needed supplies if he was to outlast his enemy. Perhaps Lee convinces Davis to strip coastal commands to form a IV Corps for Beauregard.