Does the City of God, in history, "continue unbroken, or [was it] so interrupted by periods of unholiness that not a single worshiper of the true God remained?"
Scripture is simply unclear between Noah and Abraham.
In the children of Noah, we see prefigured the City of God and the city of man, as well as a lesson on how to read Scripture in general [a lesson which I do not completely buy, but which is at least worthy of discussion]:
The object of the writer of these sacred books, or rather of the Spirit of God in him, is not only to record the past, but to depict the future, so far as it regards the city of God; for whatever is said of those who are not its citizens, is given either for her instruction, or as a foil to enhance her glory. Yet we are not to suppose that all that is recorded has some signification; but those things which have no signification of their own are interwoven for the sake of the things which are significant. It is only the ploughshare that cleaves the soil; but to effect this, other parts of the plough are requisite. It is only the strings in harps and other musical instruments which produce melodious sounds; but that they may do so, there are other parts of the instrument which are not indeed struck by those who sing, but are connected with the strings which are struck, and produce musical notes. So in this prophetic history some things are narrated which have no significance, but are, as it were, the framework to which the significant things are attached.The point of Scripture is to teach us what matters about God and His City--if there is anything there that seems superfluous, it is there to highlight what does matter. I would rather say that if there is anything there that seems superfluous, it is because we lack the wisdom/holiness to understand what it is trying to teach us.