Is String's subscript O(n) when given a lot of combining code points?

That's right. I mentioned that in the other thread about startIndex in standard library collections:

As you say, Character needs to copy its underlying data, and there can be a varying amount of data from character to character, so not all characters will take the same amount of time to access via the subscript.

However, it is still independent of the length of the entire string; the same character won't take more time to access if it were part of a longer string. That's what (I think) we mean by O(1) in this context.