Traditionally, Sinosphere countries like present day China, Korea, Vietnam etc didn't have nobles in the same sense as European feudal nobility. Feudalism with vassalage as known in Europe was largely displaced after the Han dynasty in the second century BC. This is because enfiefing nobles was seen to as the cause of most of wars in previous centuries (the Spring and Autumn, Warring State periods)

Centralised bureaucracy was the order of the day, that assigned magistrates to different levels, think a mixture of early Republican France, and the Roman empire. Positions of office were in selected based upon a massive national imperial exam system called the 科举 (Keju), at least in theory, rather than hereditary. The contents of these examinations would vary from period to period, but it would largely be focused on the 四书五经 (Four books five classics) with some military matters, law, agriculture, and geography. These bureaucrats would become China's "nobility", while in theory it was a meritocracy, we know that the successful candidates were largely from a smaller affluent social class due to the economic hardship of affording an adult male to study.

So its safe to say the nobility were fairly educated men of with diverse education, most of the famous poets, polymaths, engineers, philosophers, scientists that we associate with China were at least an aspirant scholar.

However, in the 17th century we are in the Qing dynasty period, where China was ruled by an ethnic minority group of Manchus (associated with Jurchen kingdoms of North Eastern China). While contrary to popular misconception, Manchus were not a nomadic people, they also had a distinctly different "caste" system. While the Manchus retained the traditional Keju, they added certain elements or at times reserved certain privileges to their own clans. Examples of this include the Eight banners, a complicated household/administrative/welfare system rooted in old Manchu clan system that eventually became a largely defunct military system by the end. It was very possible to be a "nobleman" in the sense you have distant clan ties to the Emperor, this would have afford you a stipend for your living in exchange for theoretical military service with no education prerequisite, not dissimilar to European nobility. However its worth noting that many Manchu clansmen did become well educated in the traditional Han Chinese way, particularly after the Kangxi Emperor who is seen to have promoted many Han Chinese customs, language and custom.