I recall during O'bama's presidential campaign, it was discovered that the birth certificate he produced was dubious.
It had certain evidence of tampering and fraud, and from this circumstance, the issue naturally arose: If Barack O'bama is not even a natural born American citizen, then he is not eligible for the office of the President of the United States.
Then he goes on the win the election, takes office, passes laws, exercises authority, legislates, etc.
There was a small fringe who nevertheless refused to recognize him as President for the aforementioned reason: One who is not a natural born citizen cannot be the President of the United States of America.
Ergo, O'bama is an imposter and a usurper.
However, to the rest of America, however distasteful we found the election of O'bama, we did not declare it invalid: He won the votes, took the office, and governed the country.
We acknowledged him as our President (a "convalidation," of sorts, even from most of those who doubted his eligibility because of the citizenship requirement).
The point regarding his eligibility was merely academic, at least to those living in the real world.
Moreover, however odious were his actions as President, he continued to be President until and unless he was impeached (which of course, he never was).
All that has been said above from the secular world of politics fits by a neat analogy the sedevacantist opinions regarding the conciliar and post-conciliar popes:
Were they heretics ineligible for office?
Irrelevant, except as an academic point (and one which I do not concede): They took office, and we consented to their rule (at least 99.999999% of the Church, and 100% of the bishops and cardinals, did).
Did they do things in office that should have disqualified them from that office?
Merely academic again: Those who could declare the fact of his deposition (i.e., that Christ had deposed the Pope, with the bishops and cardinals merely announcing that fact) have not done so.
Francis continues therefore to be a Pope (despite the many reasons he should not be), ruling and running the Church right into the ground.
Most people who live in the real world, and are not so deeply buried in the minutiae of the manuals, accept that, while a small fringe and irrelevant group deny and reject his authority based on a disputed (and in truth, misunderstood) academic point.
Was America without a president the 8 years that O'Bama usurped the office of President (if he did usurp it)?
No more than the Church has been without a Pope since 1958.