Does a divorce take effect if the husband, erring in repeating his wife's words, said, "By God Almighty, I think you are divorced," when he did not intend to initiate a divorce?

You must completely ignore these whisperings (waswas). Reporting a divorce without intending to enact it has no consequence, because one of the pillars for divorce to occur, according to jurists, is intention. And since the husband did not intend to enact the divorce, it has not occurred.