Buddhism had its roots in India, not China. As a result, it was occasionally viewed with suspicion by the Chinese imperial government. In the long run, however, it was embraced by the emperors; even Tibetan Buddhism had strong official support during most of the Qing dynasty. On an international level, therefore, Buddhism is often identified with China.
The current Chinese government is, of course, officially atheist. However, it is firmly nationalist, and (unlike Trump) it seeks soft power anywhere it can be found. There is little about the Chinese political system for a freedom-loving American or European to admire, and Chinese culture, with the exception of martial arts movies and food, doesn’t have much of a following, either, due largely to the difficulties presented by the language. The Chinese government has consequently promoted Buddhism as a way to project soft power throughout the world.
Will it work? As long as Buddhism remains out of the religious mainstream in the west, and is popularly identified with the struggles of the Tibetans, probably not.