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Yes, She does, because that's what EENS means.  We MUST uphold the doctrine that all those who die outside of the Church cannot be saved.  This is a general principle.

We only have to affirm the positive, not the negative.  What we must affirm is that there's no salvation outside the Church. What we don't affirm - and what the Church doesn't affirm - is that all those, or any one in particular, who dies visibly separated from the Church, and objectively in schism, is damned. 

But the Church does not say person A is condemned (specifically).  But She does say they cannot be saved, generally speaking.  These 2 principles are not a contradiction because salvation is a mystery.

I agree, but the way I would phrase it is that to be saved, a person must be united internally to the Church perfectly and in re, and must be united to her externally at least in voto.

Maybe it won't prevent salvation, maybe it will.  The dogma of EENS skews the answer to they will not be saved, but we don't know.

Material schism will definitely not prevent salvation.  That is certain, since material schism, as such, is not a sin.  It could indirectly prevent salvation if, for example, the schismatic in good faith received invalid absolutions due to his priest lacking faculties, but it will not directly prevent salvation, since material schism, as such, is not a sin.

There's no dogma that says I must believe those in material heresy can be saved.  Ridiculous.

I agree, but it is a dogma that baptism confers faith, hope and charity on those below the age of reason (and above the age of reason if not obstacle is placed in the way); it is also certain that faith, hope and charity are only lost by mortal sin, and that those who die with faith hope and charity (in the state of grace) are saved.  Since it is also certain that material schism is not a mortal sin that deprives a person of faith, hope or charity, we must affirm that material schism, as such, does not prevent salvation.   

If they weren't guilty of heresy/schism then they are catholic and not schismatic.  But only God knows this.  If they were "visibly" attached to a schismatic/heretical church (and not reconciled to the Catholic Faith) then we must proclaim their salvation is in doubt.  Only God knows.

But if the baptized individuals who are not guilty of heresy/schism are Catholics, it would follow that Protestants in good faith - who belong to a Protestant denomination - would be Catholics. Is that really what you believe?  That's not what the Church teaches, since a Protestant in good faith still has to formally convert to the Catholic Church to be confirmed, for example. 

In my opinion, the best way to explain it is by using the body/soul distinction, as Pius X does in his catechism. This is how he explains it:

21 Q. What is the constitution of the Church of Jesus Christ?

A. The Church of Jesus Christ has been constituted as a true and perfect Society; and in her we can distinguish a soul and a body.



22 Q. In what does the Soul of the Church consist?

A. The Soul of the Church consists in her internal and spiritual endowments, that is, faith, hope, charity, the gifts of grace and of the Holy Ghost, together with all the heavenly treasures which are hers through the merits of our Redeemer, Jesus Christ, and of the Saints.



23 Q. In what does the Body of the Church consist?

A. The Body of the Church consists in her external and visible aspect, that is, in the association of her members, in her worship, in her teaching-power and in her external rule and government.



24 Q. To be saved, is it enough to be any sort of member of the Catholic Church?

A. No, to be saved it is not enough to be any sort of member of the Catholic Church; it is necessary to be a living member.



29 Q. But if a man through no fault of his own is outside the Church, can he be saved?
A.  If he is outside the Church [i.e., outside the body of the Church, which is the visible Church] through no fault of his, that is, if he is in good faith, and if he has received Baptism, or at least has the implicit desire of Baptism; and if, moreover, he sincerely seeks the truth and does God's will as best he can such a man is indeed separated from the body of the Church, but is united to the soul of the Church and consequently is on the way of salvation

1) You can't be in formal submission to something that doesn't exist.  During an interregnum, Catholics who await the election of the new Pope by the Cardinals are in potential submission to the Pope, but not formal submission.  2) It depends on why the person is mistaken.  Is it because the person was a missionary in America in the 18th century, and didn't know that the former Pope died and a new one had been elected (as in the case of Juniper Serra), or is it because the person rejects the Pope that was elected by the Cardinals and accepted by the entire teaching Church, and instead accepts another, or no one, as the legitimate Pope?  In the latter case, the "mistake" would not constitute formal or potential submission to the Holy Father, nor would it excuse the person from his failure to do what is absolutely necessary for salvation.

Wow! That statement betrays a deep ignorance of the Western Schism and how the Church resolved that crisis. As say this as one formally trained in Church history (graduate degrees) as Ladislaus can verify.

In my opinion, the best way to explain it is by using the body/soul distinction, as Pius X does in his catechism. This is how he explains it:

[ . . . ]


29 Q. But if a man through no fault of his own is outside the Church, can he be saved?
A.  If he is outside the Church [i.e., outside the body of the Church, which is the visible Church] through no fault of his, that is, if he is in good faith, and if he has received Baptism, or at least has the implicit desire of Baptism; and if, moreover, he sincerely seeks the truth and does God's will as best he can such a man is indeed separated from the body of the Church, but is united to the soul of the Church and consequently is on the way of salvation

On the way of salvation, indeed.

Notice that it did not say that they would die in such a state.



https://stevensperay.wordpress.com/2012/12/04/fr-michael-muller-c-s-s-r-taught-the-doctrine-of-baptism-of-desire/

Fr. Michael Müller also wrote a catechism titled “Familiar Explanation of Christian Doctrine.” He writes:

Q. What are we to think of the salvation of those who are out of the pale of the Church without any fault of theirs, and who never had any opportunity of knowing better?

A. Their inculpable ignorance will not save them; but if they fear God and live up to their conscience, God, in His infinite mercy, will furnish them with the necessary means of salvation, even so as to send, if needed, an angel to instruct them in the Catholic faith, rather than let them perish through inculpable ignorance.

St. Chrysostom

Homily 60 on the Gospel of John


https://www.newadvent.org/fathers/240160.htm

John 10:16


For other sheep also I have, which are not of this fold, them also must I bring.

Observe again, the word must, here used, does not express necessity, but is declaratory of something which will certainly come to pass. As though He had said, Why marvel ye if these shall follow Me, and if My sheep shall hear My voice? When you shall see others also following Me and hearing My voice, then shall you be astonished more. And be not confounded when you hear Him say, which are not of this fold , for the difference relates to the Law only, as also Paul says, Neither circuмcision avails anything, nor uncircuмcision.

Them also must I bring. He shows that both these and those were scattered and mixed, and without shepherds, because the good Shepherd had not yet come. Then He proclaims beforehand their future union, that,

They shall be one fold.

Which same thing also Paul declared, saying, For to make in Himself of two one new man. Ephesians 2:15