Do some native English speakers recite English words in order to learn them?

For learning new words or for pronunciation - no. Reciting words is a method used to learn a second language when outside of that language's environment.

When within the language environment, new words are learned through frequent encounters with them in context. Meanings are not usually check in dictionaries but rather inferred through context.

Foreign language learners are deprived of the frequent use of the language and have little context to observe the words and meanings - thus dictionaries and repetitive recital of the worlds can aid learning.

For writing and spelling - yes. Many children are taught spelling by writing the word many times over and over. Spelling bees are a popular form of competition in the US and children will recite words and spelling to practice for these events.