No, literacy is not a part of language acquisition. Language acquisition is purely that -- acquiring language. Acquiring. You can't acquire literacy. There is no universal brain mechanism for acquiring the ability to read, that occurs without intervention in everyone surrounded by a print-rich environment.
Literacy is a part of becoming proficient in a language, if your goal involves reading and writing. There are, however, plenty of people who want to acquire Chinese without being particularly concerned about reading and writing, or about writing (some want to be able to read but aren't worried about writing). And there are all points along the spectrum of writing, too: written by hand from memory, by hand from a writing aid, by computer).
Chinese literacy -- learning to read and write Chinese -- is more challenging than learning to read and write an alphabetic language, obviously. There is not as easily circumscribed a set of symbols where you can say "There, I know those!" It is more challenging (though getting easier with modern technology) to find information about unknowns in a text (well, I learned to read back in the 1980s when it was about an 80% probability I would be able to find any given character in the dictionary if I wanted to look it up and didn't know how to pronounce it; contrast that with today's Pleco dictionary and its character recognition from photos!) But still not as simple as dealing with an alphabet.
The methodological comments still hold, though. It is far, far easier to teach someone to read a language that they are fluent in than to get them to read a language they haven't mastered -- yet that's what is done in most Chinese classes. Students are required to read (often out loud) language they have barely begun to work with. It's not "in their heads". They can't read a sentence and stop and say, "Hey, that last word doesn't make sense there. Let me look at that character again and make a different guess." That is the kind of error correction we are seeing when teaching reading with CI-friendly methods. It was really exciting to see novice-level Chinese students reading and actually getting impatient when we'd ask them what a sentence meant. "Duh! I know what it means. I'm just trying to read it!"
To do that, though, at present teachers have to actually write the reading materials, OR start with the reading materials already selected and teach the language included in the readings, specifically. You could get the same effect using the standard textbook "reading passage" if you took the time to have students really acquire the language before reading it, but that's not part of the communicative teaching model, so that's not what happens the majority of the time. And so it is that Chinese literacy is made more difficult than it needs to be.