Ken says it is "a slog". I'd say it is almost humanly impossible. If a group had a number of days, with more than two or three individuals to take turns breaking trail, then they might succeed. But it still wouldn't be any fun.
As for consolidating, I think snow settles some even without melting -- the air spaces can compress some, but only to a point. In the White Mountains Sunday and Monday, there was a north-facing slope that had obviously not seen any temps above freezing for several months. Stepping off a sled, we'd sink up to our hips. Trying to pack a trail took a huge amount of energy. We could compact the snow a bit, maybe 18 inches.
But in the worst places, the snow would NOT consolidate. There were several times that I'd try to get solid footing, but placing my feet side-by-side and alternate weighting and unloading each foot, the snow was like quick-sand. It just gave way under the weighted foot, only to spring back when the other foot weighted the adjacent area. Cold sugar-crystal snow would be impossible for foot travel.
The Mountaineers Route is so much shorter, so each step breaking trail is three times as effective as a step on the Main Trail route. And then, with so many people going that route, there is already a boot track to follow. Much nicer!