Yes, because the Army of Tennessee will run out of supplies by being at Knoxville. Seriously, this is not a video game where supplies are abstract in nature. We know the supply shortages Longstreet's Corps badly suffered during the Knoxville Campaign.
Supplies can come through the East Tennessee & Virginia Railroad, but Lee's army is getting first pick for both food and materials. Since Virginia's depots were already empty on Lee's needs, supplies towards Knoxville had to be sent from Georgia in a roundabout way - which is going to happen if your enemy still occupies Chattanooga! It was so bad that it was even recommended to Longstreet to either rely on forage or evacuate East Tennessee.