When I had to register my old China Mobile SIM, the CM stores wouldn't handle it: they sent me off to the take-a-number-and-wait (and wait) customer service centre. So I assumed same for buying a new SIM and same for Unicom.
That was my guess too, but my colleagues told me I was mistaken, and were correct. That having been, I think the airport premium is probably worth it these days. If nothing else, you can at least get caught up on emails during the ride into town.