If Chu had managed to unite China, these would be the possible consequences:
1. Since the capital and the political power are far down south, the need of a wall defense against the Northern barbarians is greatly reduced; So there would be probably no Great Wall, instead we might get a early Great Canal facilitating the north-to-south transportation. In general, the spotlight of Chinese civilization would shift south; Chu would probably encourage the mass to migrate and populate the vast land of the south, leading to an earlier development of the Yue areas including Fujian, Hunan, Guangnan, and Nanyue(Vietnam).
2. Daoism would be favored over Confucianism; Laozi was from Chu, and his theory was popular among Chu scholars.
That's what would be a profound effect on the development of Chinese civilization.
3. The language development would change course drastically. Chu language is noticeably different from all other contemporary languages spoken in the northern states, with much characteristic of tribes south of the China proper, and many unique words. Following the Chu's ascendance, this language would become official and would have a much greater effect on the northern dialects than in OTL.
4. Ceremonial rituals would be more prevalent in Chinese lands. In Chu, Shaman women (or Miko, with Chinese style) had led vibrant rituals to please the gods, with dancing and singing, much like the cultures of the various ethnicities in SW China. Chu would certainly promote their unique bit of culture to the north.
That's what I can think of for now, and please do point out any mistakes I've made