EDIT: This answer refers to the initial version of the question. After this answer was written, user JohnWDailey modified his question moving the date of the hypothetical conquest from the 3rd millenium BCE to the 3rd century BCE. This answer is of now of course obsolete.
In the 3rd millenium BCE there were no Mongols and no Chinese, and there was nothing for the ancestors of the Mongols to conquer in the lands which would eventually belong to the empire we call China.
The Chinese do not call themselves Chinese (the most numerous ethnic identity is Han) and they do not call their country China; see names of China. The most common native name is Middle Kingdom or Middle State, pronounced in Modern Standard Mandarin Zhongguo (in Pinyin Romanization) or Chung-kuo (in Wade-Giles Romanization); in the 18th and 19th century the preferred name was the Celestial Empire. In European languages we use either a name derived from Qin (Ch'in in Wade-Giles), a state which existed in the western part of what is now China from the 9th to the 3rd century BCE, or a name derived from Khitan, a people which conquered the northern part of what is today China in the 10th century CE, and later established a state in Central Asia. From Qin we have China and Chinese in English and similar names in Frech, German, Italian, Romanian, etc. From Khitan we have Cathay in English, and similar names in Portuguese, Spanish, Russian etc.
Nations are not natural phenomena, they are purely political and historical constructions, emerging from a community of language, history and economy over a long period. In the real history the first recognizable "Chinese" state was created at the end of the 3rd / beginning of the 2nd millenium BCE: the Xia (Hsia in Wade-Giles), which ruled over an ill-defined territory we believe was somewhere on the lower course of the Huang He / Yellow River. The earliest Chinese state for which there is solid evidence emerged towards the middle of the 2nd millenium BCE in the Yellow River valley: the Shang dynasty. The first emperor of a unified state was Qin Shi Huang in the 3rd century BCE; he conquered (or united, if one prefers the nationalistic view) and ruled over what is today northern China.
The middle-of-the-3rd-millenium BCE conquest proposed by the question would have happened during the mythical period of the Three Sovereigns and Five Emperors; the mythical history of China begins with the Yellow Emperor, Huangdi (Huang-ti in Wade-Giles), a figure about as historical as Hercules or Perseus.
It is also important to note that the Mongol "conquest" of China in the 13th century was more in the nature of a struggle for power. For the vast majority of the people is was of limited importance whether the emperor belonged to the Song (native) or Yuan (Mongol) dynasty. It was not Genghis who did it, but rather his grand-grandson Kublai Khan (in Xanadu did Kubla Khan a stately pleasure dome decree...), who promptly declared himself Chinese emperor (in Chinese terms, he "proclaimed the mandate of Heaven") and founded the Yuan dynasty. The influence of Mongol culture over the Chinese culture is somewhere between none and almost none.