Does a final, irrevocable divorce (talaq bain) become revocable (raj'i) if the husband says to his wife: "If you have committed any treachery, then you are irrevocably divorced with a final divorce (talaq bain la ruj'a fih)," while intending in his heart that it be a revocable divorce?

You must have a good opinion of your wife and not accuse her based on suspicions or satanic dreams, because the default is the innocence of a Muslim. Islam has forbidden ill-suspicion, espionage, and a man's distrust of his wife. Furthermore, conditioning divorce upon what you have accused your wife of is wrong, but it has not taken place as long as the wife denies it, because a divorce conditioned upon a matter does not occur unless the wife acknowledges it.