Last time I was in China (late 2014) I had to provide a photocopy of my Australian passport to obtain a China Mobile SIM. Maybe it's changed since then, but I certainly can't imagine them being any more liberal than Australia, where you are required to submit a driver's licence number or a similar level of identity verification in order to activate a prepaid SIM.

That said, I can't imagine it being too hard to bribe someone to get a SIM not linked to an ID if you really wanted...