A great viev on that problem is given in F.W. von Mellenthin's book "Panzer Battles".
Manstein during his counteroffensive reached the point 64 km far from von Paulus lines. He (von Paulus) gave an order to commence march ahead approaching forces when they would be 32 km away. Manstein has never reached such a distance, so the didn't even try to break out. Germans hadn't enough forces and supplies to establish route to Stalingrad.
Even if the 6th army had been saved, it's remainings wouldn't have been able to take serious operations for a long time. They would propably have been evacuated to France or Germany to reinforce or destroyed in incoming Russian offensive. How sid wrote, russians would be much sooner able to endanger Rostov. Moreover, if Russians hadn't had to use so many divisions around Stalingrad, they would propably have been sent to cut off von Kleist's 4th Army retreating from Caucasus. It has been written in many books, that sacrefice of 6th Army save the 4th.
So: even if Manstein had been able to brake and save a part of 6th Army (without most of it's heavy equipment, but with many highly experienced soldiers), the 4th Army would propably have been destroyed and Red Army would sooner have reached Rostov.
Don't worry, be crazy ;]