Yes, and that objective truth acts like a seed on those of good will - and leads them to be CONVICTED TO ACT upon that truth (moral certainty).
Once the act of separating from the false Popes is consummate in its entirety (and this is KEY) then one is in full possession of the objective truth in this matter and the subject has become reconciled to the objective truth in this case, as you say, "that a true pope cannot promote to the universal Church anything harmful to Faith or Morals."
There is ALWAYS the subjective element to accepting the objective truth. But we MUST STILL PRESENT THE OBJECTIVE TRUTH AND SAY IT IS.
The objective truth is that nobody can find Our Lady's mortal remains on earth in some archaeological site.
Likewise, the objective truth is that papal claimants since Vatican II cannot be true popes if they promote the heresies of V2 to the Church.
Not a dogma, but as certain as a dogma, so the certainty is as certain as the Faith itself.