Well, often they can't write these characters at all [1] (this video is for Japanese, but the situation must be similar with Chinese)

[1] https://www.youtube.com/watch?v=sJNxPRBvRQg

I can recognize more than a thousand of characters (thanks to Anki) but visualising/writing them is another matter entirely, and I would probably fail to write a large fraction of them. Just like with alphabetic characters, I memorize the "shape" of the character rather than its sequence of strokes. Only when the character is indistinct, or similar to other characters do I bother to remember which radicals it consists of.

For example the character for "dream" (夢) has a very distinctive shape that is easy to recognize, so I wouldn't be able to write it because I never learned how.

Now take the character 緑 (green). It looks similar to 線 (line), but lacks the radical 白 (white). Because green is not white, you see (not actually, it's just a memorization technique). But it also looks similar to 録 (recording). That's because the character for "green" has radical 糸 (thread), just like "line" character. Threads can be green, and they are also lines. But "recording" uses radical 金 (metal) in its place, because recorders are made from metal. So the only things I remember about 緑 is that it has 糸 and doesn't have 白. And thus, I still won't be able to write it.