China depends on exports for a sizable amount of employment, and so I would argue it doesn't have much leverage through exports - in fact its rather the opposite.

Regardless, China would have a hard time competing with the US in influence should the US decide to compete in a certain area. For example, if civil unrest or war would to erupt in Africa/Latin America, the US has the multi-faceted resources (military, diplomatic, money, etc) to make a huge impact, whereas China doesn't have those same resources, maybe only the promise of economic aid.