Speaking as someone who has done this (I live in Taiyuan, Shanxi), I can tell you that the 360 will work if you get a 220V power brick and simply swap it out. Make sure that you match the brick to your model (normal or Slim). You can connect to Live and continue to download from the US store, but you need a US Visa or MasterCard to fund it (unionpay is not accepted). It gets annoying when you login by PC and have to enter a code, but your system will work. Net speeds are kind of the pits in some places, so you may want to go wired.
Remember that neither games nor DVDs you buy in China, Taiwan or Hong Kong will work on your US 360. So bring games with you or buy via the Marketplace.