IMO, China's innovation is in large-scale PCBs and other such manufacturing. See Apple's investment of CNC machines in China as an example. China has several other innovations that does in fact make them a world leader in certain fields.
As far as battery tech goes however, Japan has that on lockdown. Panasonic's Silicon-Lithium batteries are light-years ahead of the competition, even as US battery manufacturers (A123 systems) try to break through. Japan (and Panasonic really: now that Panasonic owns Sanyo / Eneloop) has all of the major high-quality battery manufacturing facilities: Energizer, Duracell, Panasonic (owner of Sanyo / Eneloop).
Korea has the next best bet as far as I can tell. LG Chem's batteries were chosen by GM probably for some reason.
If China were to be making good batteries, then we'd first see some manufacturing companies make some batteries. Most "top-down grown" companies, be in the USA or China, fall flat on their face for the first few decades. It takes a long time to build up expertise.
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There's no reason why China can't grow into a battery powerhouse. Except for the fact that Panasonic is so massive.