The war is won with Intel, i think the theory that Eddard would march with around 10.000 is accurate he wouldnt pull all the troops with him.
Once they arrive at the wall, the Nightwatch woulf function as eyes and ears and Mance would eventually end up in trouble. As their fighting at the wall showed they have no organization or teamwork, they fight as individuals instead of an unite, so odds 4:1 againt Stark is not too bad. They just have to hit the Wildlings Hard and Fast and they would crumble.
The X-Factor are the Others, Mance cannot turn back from whence they came, winter has come and they have cleared the land of food going forward, and if they were forced to retreat lots of fresh corpses to rise in the hands of the Others.
So If Mance becomes aware of the Eddard force, he would Parley, make a show of how many men he has ands then negotiate settlement at The Gift, if that fails then combat and the chaos that will lead too.
Just my two kroner on the subject
