Right. When Farragut occupied the confluence of the Red River with the Mississippi, and the Confederates had to deal with Rosecrans movement in central Tennessee, their logistical ability in the west began to collapse. The consequences were felt at Chattanooga.. Wheeler's cavalry could not stay north of the Tennessee River. Longstreet's divisions could not be supplied far to the west of the railroad, and they had to be relocated.
The regiments aligned by the Confederates on Missionary Ridge were questionable. Some were improperly exchanged survivors of Vicksburg, and others were not being properly fed. And in his Memoirs Grant related stories casting doubt on the willingness of these Confederate westerners to die for a cause that was definitely lost in the west.
The Confederate outposts along the Tennessee River were very passive. The Confederates did not fight very long for their Orchard Knob position. The Confederate position on Lookout Mountain had no limbs and Hooker and his amalgamated divisions did the right thing and threatened to cut off the Confederates.
By about the 25th of November, the US troops had doubts about the Confederates in front of them. These doubts were only confirmed when the Confederates gave up the trenches in front of Missionary Ridge, and scurried up the ridge.
The railroads were only one of the Confederate problems. When the US restored full military use of the Mississippi, and the Confederates were expelled from Kentucky and Tennessee, even a better railroad system was not going to save them from their lack of the physical quantities necessary to sustain their military livestock.
And as
@DaveBrt notes, even if the Confederates had the railroad equipment, the steady loss of territory, the weight of conscription and the leakage of the fittest and most able part of the formerly enslaved population to the US, was going to make maintenance of the Confederate railroads a difficult task.