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Yes, writing increases the modality and attention given to a piece of information. Increasing the effort and the ways that you have experienced a bit of information helps you encode that information better; this is Elaborative Encoding.

More generally the more deeply you process a thing the more likely you are to properly encode the memory for future retrieval. Simply looking at characters is very shallow processing; writing and constructing them is relatively deep. This is the Modality Effect.

Explaining how things work and showing others or doing a task is also a much better way to remember things than just reading about them; in the case of remembering Chinese Characters there's less you can do other than write them, but practice methods like writing a brief paper can help you learn to use them. This is why essays are a common task in language classes.

Note however that Transfer-Appropriate Processing is also relevant: retrieval is more likely when we attempt to retrieve information in a similar or appropriate context to when encoding occurred. Therefore writing symbols could arguably be a bit less appropriate way to learn to read symbols; however it is an extremely relevant way of learning how to write and construct those symbols.

I've found some general reference sites eluding to this effect such as this post on Lifehack: Writing and Remembering: Why We Remember What We Write, but could not find experimental results supporting this specific idea. I know my advanced course on Memory covered this specifically but I don't recall exact studies.