Not historian, but read history in school. My educated guess is, no, at least not in official capacity. The earliest record (that was taught in school) of exchange between China and the West Regions (西域) was Zhang Qian 張騫, who was born 200 BC, in the Han Dynasty, over 100 years after the fall of the Achaemenid Empire. Zhang was credited for establishing the silk road, before which time, traveling in that region was impossible (frequently raided by Xiongnu). Zhang only reached as far as Uzbek/Afghan.

For 100 years before his time, China was mired in civil war, expedition to the far west was probably not on many people's mind. And further back in time was Zhou Dynastic, where written records are few and sketchy.

Source: History classes in Chinese High School.