Yes, but when you need different traits in the same culture group the culture type is not enough. For example,in Inca:Total War the Aztec and Mixtec are in the same culture group, but the Aztec faction leader is called 'Hueyni Tlatoani' while the Mixtec one is called 'Cacique'.

off topic: according the spell corrector Hueyni Tlatoani is an error while Cacique is a proper English word .