Does imitation play any role in child language acquisition? In the 1950s/1960s, there was a debate between Skinner and Chomsky, in which Chomsky argued that children also produce sentences that they have not heard spoken around them. In other words, imitation is not the only factor in first-language acquisition. But what is the role of imitation according to sociolinguistic and/or psycholinguistic research since Chomsky?
Imitation is an instinctive behaviour found in not only humans but other animals also. An obvious example would be parrots. So, naturally, children will learn languages through imitation of other native speakers. However, languages can also be acquired through reading and writing alone such as in the example of deaf-born individuals. Many may argue that one can also imitate what they read by writing it themselves but I assume you are referring to oral and auditory aspects of learning.
Personally, I believe speech, in general, is an imperative factor in learning languages for both children and adults and must never be neglected nor forgotten but that is certainly not as to say that language is impossible without it as before the first languages existed, who had the first linguists immitated to learn it?
I am a polyglot (speaker of many languages) so my references are mostly based on post-childhood studies such as Lydia Malchova who wrote an article about self-talking to improve speaking without communicating with anyone else who speaks the language:
And also on a completely parallel point of view, fluentin3months (another polyglot) has an article relating to passive learning which is merely listening and not speaking, reading or writing:
I sincerely hope this helps and look forward to hearing other answers since this is purely from a linguistic point of view as opposed to that of a psychologist or child behavioural analyst :)