Apart from that in reality Manstein was still very far from his goal when he was stopped, a very interesting preposition!
The first thing that it would have brought for sure is a tremendous boost to German morale. Churchill was right that wars are not won by successful evacuations, but such events have always given new confidence. On the other hand it would have been bad for Soviet confidence and it might be that heads of generals had rolled in consequence.
But from the military point of view, the advantage for the Germans would not have been as great as it first seems.
The number of encircled troops in Stalingrad was truly impressive, but a successful relief operation by Manstein, would by no means have meant that all of them, or even the better part of them would have once more been available for battle. As the corridor to the encircled troops would only have been defendable for a very limited time, not only would all heavy material have to be abandoned, but also the numerous sick and wounded, (even those only slightly wounded, as this would have turned into a forced march by foot escape). Apart from that, the red army would not have taken such an event lightly and would have fiercely attacked and shelled the escaping collumns leading to plenty more casualties.
Second comes that instead of making an orderly retreat with most of their heavy material which was enabled by the prolonged resistance of the 6th army in its surrounded position, the panzerarmee of Hoth in the South would have to make a run for it, losing much valuable material.
Above all that comes that Mansteins position after relieving the Stalingrad troops would have become less then enviable. What makes mass encirclements like the one at Stalingrad such foremost military feats is the fact that the attacking party needs massive amounts of troops and materials as it has to contain the encircled enemy on all four sides. Now, even if the Germans had arranged for a well constructed defense line for Manstein to fall back on things soon would have gotten pretty hot there. The tremendous shortening (and shift westwards) of the front caused by the evacuation of Stalingrad, would have been more to the advantage of the pursuers than of the attackers as they could concentrate all their might on the shortened frontline. On the other hand the Germans would have to do with what was at hand anyway: Given the mauled status of the 6th army few of its units would be in condition for serving as direct reinforcement of the new, lets call it "Manstein line", while the original troops would have pretty much suffered in their relieve offensive.

However, like I said at the beginning, it would have been tremendously interesting to see what would have developed in case this scenario had indeed become reality!