I’m still pondering if your first sentence is true, but in any case, China already IS an economic powerhouse (#2 in the world, in fact). So by all means, by your definition, it’s–at the very least–ready to become a cultural exporter.
As to whether or not people are ready to consume Chinese cultural exports, I think they are. However, it’s long been a consumption of mostly superficially/stereotypically Chinese cultural symbols. This is, of course, partially the fault of the Chinese people themselves as they are eager to feed the West with low-margin, low-value goods. Again, self-reflection and an willingness to develop a sophisticated design mindset will be required.
The Chinese are developing very quickly in the mold of Western design. In the arguably most visible field of car design, domestic companies are rapidly improving their designs (if not quality). Both the Japanese and subsequently the South Korean brands quickly caught up and in many cases exceeded Western designs; it won’t take long (within 10 yrs, I’d say) for the Chinese to make equally dependable and good-looking cars. What I would like to see happen, though, is for Chinese design to not simply “look better” and “sell at a lower price” than Western design. Chinese design has a real opportunity to be something more and something that can benefit design as a whole, and NOT be the focus of simply being cheaper than everyone else. I think we’re on the cusp of that change; if we wait too long, then China will simply be America: the Second Coming. Times 10. Given the planet’s limited resources, that’s not what the world needs.