If Bergoglio were to come out and confirm this heresy, there would be no need for any declaration by the Church. This is where S&S are wrong. When it's obvious and blatant like this, there's no need for any formal declaration, since all Catholics would simply recognize that this man is not one of us. S&S muddied the waters with their shoddy work.
What effect would any declaration have? Since the Church cannot judge the pope or juridically convict him of anything at all, it would only be a clarification regarding the mind of the Church. It only serves a purpose where perhaps the Church might be divided and not unanimous, or where there was any disagreement over whether a particular proposition was actually heretical. Such a declaration would have the effect of the Church "making up her mind" on the matter ... and that's it. In a case like this, where Bergoglio were to deny the Divinity of Christ, he would be non-Catholic and a non-Pope without any declaration. S&S falsely drew the line at "apostasy" due to bad theology.
I think S&S clarified the waters, rather than muddying them:
Their doctrine is nothing more than a restatement of JST, and they pointed out that the only difference between JST and Bellarmine was whether or not a SECOND DECLARATION by the Church was necessary to declare Christ had deposed the pope (while BOTH AGREED the Church would have to declare the fact of the pope’s heresy).
So the idea that a pope is deposed ipso facto for heresy without a declaration of the Church is supported by nobody.
But that novel and unsupported opinion is exactly what you are proposing (and it is obviously ruinous and incompatible for the unity of the Church to have a Protestant private interpretation by private individuals determining subjectively whether or not there is a pope.