I know it is not a sacrament but it has not been condemned by Saint Alphonsus. He declared it de fide based upon Trent. You are unable or unwilling to see that BOD does not contradict EENS but compliments it.
If you know it's not a sacrament, and you know Trent condemned anyone says that the sacraments of the new law are not necessary for salvation, then you know a BOD without the sacrament cannot save anyone because it is not a sacrament.
Further, St. Alphonsus echoed Trent when he said that heretics say the sacraments are not necessary, then you know you are condemned by Trent for claiming a BOD saves without the sacrament and a heretic per St. Alphonsus for saying a person without the sacrament can still attain salvation via a BOD.
Either way, Trent is the Church, St. Alphonsus is not the Church, he made a mistake, the Church did not, he demonstrated that he submitted to the judgement of the Church when he finally taught:
"The heretics say that no sacrament is necessary, inasmuch as they hold that man is justified by faith alone". Faith alone" = a BOD.