If Jorge Bergoglio publicly admitted that he is a heretic and none of the cardinals or bishops did anything about it, would you still consider him to be pope?
No.
In that case, a declaration by the Church of the fact of heresy would seem unnecessary:
The purpose of the declaration by the cardinals is to announce the fact of the pope’s heresy. Therefore, he’d basically be doing that for them.
At that point, either St. Bellarmine would kick in (ie., deposition by God from the moment of the declaration), or, per Cajetan/JST et al, the deposition would occur at the moment of the second declaration (ie., of his deposition).
Either way, the only question would be the timing of the deposition (between the 1st and 2nd declaration), sede vacante either being the case, or an imminent inevitability.