I would say, "no," but perhaps that's just me. Let's just say, assuming you want to check out some alpine lakes and/or Turpan, what you're talking about is akin to visiting the Grand Canyon from New York with only 2 days at you're disposal; sure, it's doable, but you'll spend much more time in motion (and on gross mini-buses rather than comfortable trains) than doing fun things.

A natural solution would be figure out a way to spend more time out west, perhaps at the expense of axing Shanghai.