No.  The loss of office takes place at the same time the authority is lost.  A declaration only makes the loss of office explicitly known.  Canon 188.4º of the 1917 Code calls this a tacit renunciation of office.

Billuart:

"Nevertheless, the more common opinion (sententia communior) holds that Christ, by a special dispensation, for the common good and tranquility of the Church, will continue to give jurisdiction even to a manifestly heretical pope, until he has been declared a manifest heretic by the Church."
(Summa S. Thomae of Charles Rene Billuart, O.P. (1685-1757) Secunda Secundae, 4th Dissertation: On the Vices Opposed to Faith, Article 3)

The relevance of Billuart's quote is that sedevacantists interpret St. Bellarmine as proposing a manifest heretic is deprived of office ipso facto (without any judgment or declaration of the Church).

Billuart is saying exactly the opposite, and more than this, is saying that it is the more common position of approved theologians (i.e., not just his own opinion).

Billuart explains the reason for this more common opinion a couple paragraphs earlier in the same article: "...the law and praxis of the Church require that a heretic be denounced before he loses his jurisdiction, not for his own benefit, but for the benefit and tranquility of the faithful.

Even more importantly, this more common opinion (which opposes the erroneous and univocal sedevacantist interpretation of St. Bellarmine's words) is sanctioned by the magisterial teaching of the Church itself in the Papal Bull of Pope Martin V, Ad Evitanda Scandala ("To avoid scandal"):

"To avoid the scandals and the many perils that can befall timorous consciences, we mercifully grant to the faithful of Christ, by the force of this decree (tenore praesentium), that henceforth no one will be obliged, under the pretext of any sentence or ecclesiastical censure generally promulgated by law or by man, to avoid the communion of any person, in the administration or reception of the Sacraments, or in any other matters sacred or profane, or to eschew the person, or to observe any ecclesiastical interdict, unless a sentence or censure of this kind shall have been published by a judge, and denounced specially and expressly, whether against a person, or a college, or university, or church, or a certain place or territory.  Neither the Apostolic Constitutions, nor any other laws remain in force to the contrary."

Note also in the following passage, that when Billuart says "or themselves depart from the Church," he means they themselves leave the Church of their own accord (not that by endorsing some heresy, they have departed from the Church):

"If manifest heretics had to be avoided before their denunciation, this would endanger souls and generate anxiety of conscience, since there would be uncertainty as to who are manifest heretics, some persons affirming, and others denying, as actually happened in the case of Jansenism.  It is very difficult for lay people to know with certainty if someone is a manifest heretic or not, since in most cases the subject-matter of the heresy surpasses their understanding.  For all these reasons, the Council prudently decided that only those who have been denounced would have to be avoided.  These reasons, however, do not apply anymore once the heretic leaves the Church of his own accord."

I think you’re misconstruing (in red above) jurisdiction with the office. The heretic loses the office ipso facto, but for the common good Christ supplies jurisdiction. With the declaration the supplied jurisdiction disappears as well.

Bottom line is that since Vatican I only Bellarmine's opinion remains standing.  It is absolutely essential that the Pope have been ipso facto deposed by God BEFORE the Church could render any kind of judgment regarding the man who used to be Pope.  To hold anything else would be to assert the heresy condemned by Vatican I that the Church can pass judgment on a Pope.