A big part of the reasoning for 6th Army to hold in place was simply the greater part of it was virtually immobile to begin with. Other than the handful of panzer and panzergrenadier units, all of which were critically short on everything, the army was foot and horse mobile.
To make matters worse, AGC and AGN had been largely denuded of equipment and replacements earlier in the year to allow offenisve operations by AGS. Thus, when ordered to relieve 6th Army these units showed up with a fraction of their full fighting strenght. 11th Panzer, a spearhead unit in the relief effort, for example had one understrength battalion of panzers (mixed Pz III and IV).

If we take a position that the withdrawal of 6th Army et al, starts earlier and the Germans attempt to form a new front somewhere to the rear of their initial positions much the same thing happens. Since the bulk of this line would consist of leg infantry units these would find themselves hard pressed to march to their new positions and then dig in for a defense in a timely manner.
More likely, they would have to abandon alot of their heavy equipment in favor of mobility to withdraw making them marginal in value for defense. If anything, the likelyhood is that the Soviets would do better in the face of a full German withdrawal due in large part to the poor mobility of the majority of the German army.