As a native Mandarin speaker, I don't tend to think of the "ten" as a ten. If anything, for me it conjures up an image of the number of 0s. So, the "hundreds" part in "four hundreds" would just means four followed by two zeros, etc. I may even have been taught this as a child; can't remember. Anyway, no arithmetic involved, at least not explicitly.

I don't know that this generalizes -- other Mandarin speakers may have a different experience. I'm really curious how Chinese-speaking people thought about these things before Arabic numerals, but not sure we can ever have a clear answer to that question.