These are a couple great articles by Brent Wilson about how children in different cultures learn to draw, particularly contrasting the Japanese with other cultures. Both articles contain more extensive discussions that I'll mention here, only focusing on some of the highlights...
Wilson, Brent. (1999). Becoming Japanese: Manga, Children’s Drawings, and the Construction of National Character. Visual Arts Research, 25(2), 48-60.
Here Wilson provides fairly striking evidence that over two-thirds of the drawings produced by Japanese children in primary education (K-6) are imitative of manga. However, even many of his "non-manga" types could have been drawn from manga and still might be drawn in that style. He also notes a developmental trajectory: There is a decline in non-manga drawings after kindergarten.
I would guess that this is in part a socialization process. Since kids at kindergarten start playing with other children in a structured arena, and all of them know manga, there is more of a motivation to draw in the style of the group than whatever way they might be drawing at home. Also, it reflects a growing sense of literacy. Since kids are learning to read, manga become reading material in addition to stimuli for learning to draw.
Wilson, B. (1988). The Artistic Tower of Babel: Inextricable Links Between Culture and Graphic Development. In G. W. Hardiman & T. Zernich (Eds.), Discerning Art: Concepts and Issues. Champaign, IL: Stipes Publishing Company.
In this article, Wilson focuses on the argument against the belief that the Romantic view that children develop an inborn "artistic" capacity and that external influences are bad for it. He compares this in part to a sort of "Tower of Babel" phenomenon, where everyone has a universal inborn "language of art" that develops uniquely suited to each individual.
His theory against these claims is that graphic symbolism is a language that is transmitted through cultural patterns imitatively. He cites numerous evidence for this from numerous countries and time periods.
Pertaining to Japanese children though, he has a fascinating note that nearly all of the 6-year old Japanese children they studied could draw coherent sequential stories, compared with other countries where only about half of some groups of 12-year olds could. He also notes that Japanese children use increasingly more complex methods of graphic narrative as they age, (examples from 9 to 12), though they are all imitative of manga techniques.
These examples support that drawing ability is learned, as well as that imitation boosts abilities rather than hampers it.