Not that accord with the early Church is necessarily an indicator of morality, but there is little to recommend Rome as an exemplar of carnal constraint, at ANY point in its history.
1. I referred to "... the century or so before [the Western Empire's] final collapse". Given that the Western Empire was finally extinguished in 476, a century earlier would be 376, a time when Christianity was well and firmly established in the Roman world.
2. I referred to "morality and religious fervor", not Christianity specifically. Cults such as the Eleusinian Mysteries and other eastern religions such as Mithraism were also extremely widespread in this period.
3. It's excessive to say that Rome never evinced "carnal constraint" at "ANY" point in its history. Traditional Roman religion was still strong as late as 100 BC, or over six centuries into the city's history, and morals which seem familiar to ours had begun to take hold with the spread of Christianity, as early as the third century AD.
But you're right. Morality isn't solely defined by Christianity. Let's just say that at its nadir, Rome was capable of the depravities described in this article, and that that level of amorality, accompanied by the subsequent decline in social and military unity, contributed substantially to the fall of the Empire. By the time Constantine (and even Diocletian) managed to recover some sense of integrity, there was little left of Glorious Rome.