Does the acceptances replace the canonical election? Does it provide a sanatio in radice as it were to the election? Or is this notion merely an infallible sign that the election must have been valid in the first place? I'm asking these questions because I'm trying to get my head around this "peaceful acceptance" issue. And then of course the issue after that will be what constitutes "peaceful acceptance".
To your questions, Gueranger writes that when the Church "acknowledges in the person of a certain Pope, until then doubtful, the true Sovereign Pontiff, this her very recognition is a proof that, from that moment at least, the occupant of the Apostolic See is as such invested by God himself. Although convalidation and universal acceptance being an effect of a valid election are conceptually distinct in theory, in practice it is of little consequence. Whatever the case, after one Pontiff is universally recognized, the ecclesia docens testifies that he is infallibly the Pope, and the ecclesia discens accepts this with ecclesiastical faith.
In other words, it can happen, of course, as it did in the great schism, that one of two persons seem to be elected, the Cardinals come out with conflicting reports, and each are accepted by a section of the Church. In this case, the status of claims to the Papacy may for a while remain truly and objectively doubtful. However, each adherent to any claimant always acknowledges that should any one claimant ever be accepted by all the bishops, that person is truly Pope, and remaining separate from him after that is unjustified. All sides admitted this during the Great Schism. Fr. Hunter writes, "it is enough to say that if the Bishops agree in recognizing a certain man as Pope, they are certainly right, for otherwise the body of the Bishops would be separated from their head, and the Divine constitution of the Church would be ruined." St. Alphonsus similarly says, ""It doesn't matter that in past centuries some pontiff has been elected by fraud: it suffices that he has been accepted after as Pope by all the Church, for by this fact he has become true pontiff."
It is said to be not only an infallible effect, but also a sign, and is easily discernible as such in the external forum, Ex Quo by Pope Benedict XIV shows us a simple means by which we can be sure, " it suffices Us to be able to state that a commemoration of the supreme pontiff and prayers offered for him during the sacrifice of the Mass is considered, and really is, an affirmative indication which recognizes him as the head of the Church, the vicar of Christ, and the successor of blessed Peter, and is the profession of a mind and will which firmly espouses Catholic unity." It also shows that no one can by private judgment before the declaration of the Church presume to drop the name of the one universally recognized as Pope from the canon, otherwise he will separate from the external communion of the Church, "It is generally agreed that those who do not for any reason recall the memory of the Apostolic pontiff in the course of the sacred mysteries according to custom are, as the blessed Pelagius teaches, separated from the communion of the entire world." Cardinal Manning wrote,
"It is de fide, or matter of faith, that the head of the Church, as such, can never be separated, either from the Ecclesia docens, or the Ecclesia discens; that is, either from the Episcopate or from the faithful ... On this unity all the properties and endowments of the Church depend; indefectibility, unity, infallibility. As the Church can never be separated from its invisible Head, so never from its visible head ... Such separation would destroy the infallibility of the Church itself. The Ecclesia docens would cease to exist; but this is impossible, and without heresy cannot be supposed."
A sedevacantist like Nado, for example, needs to show that at least one bishop, but probably much more (since we are talking only of moral unanimity of acceptance) who openly contested Pope Paul VI before the end of 1965, otherwise the sedevacantist explanation of the Second Vatican Council is incorrect.
As a matter of fact, no bishop did so at the time, not even Cardinal Siri. I don't doubt personally that Cardinal Siri really was elected, but the fact that Pope John XXIII was universally accepted proves that, at least after that moment, his papacy was no longer doubtful, but infallibly certain. In the conclave that elected Pope St. Pius X, there was external interference as well. But no one, on that account, adhering to another claimant, could justifiably refuse to recognize Pope St. Pius X, after he was accepted by the Church. Likewise, after it became evident that Cardinal Siri and the whole Church publicly accepted the Pope, no doubt could remain anymore, and the visible teaching Church or ecclesia docens, as Cardinal Manning and Fr. Hunter says, by their unanimous acceptance of a single candidate, constitute a sufficient and infallible proof that the Pope was really the Pope, even after that time when sedevacantism requires that he was not. Therefore, this teaching shows that sedevacantism/sedeimpeditism/Sirianism etc are all incorrect explanations.