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Do I understand you correctly, Hermann, that a baptized (in a Protestant setting, but validly) Protestant is a capital-C Catholic Christian who fell off on the rest of the sacraments?

Yes. Everyone who is baptized is baptized into the Catholic Church, because there is only one Baptism, and one result of Baptism. Being Baptized among heretics makes Baptism inoperative in terms of bestowing grace, unless it is done in infancy, because heresy is inimical to faith, and without faith, no one can be justified. This is why the great Doctor, St. Alphonsus de Liguori writes:

"We must believe that the Roman Catholic Church is the only true Church. Hence, they who are out of our Church, or separated, cannot be saved, except infants who die after baptism." (On the Commandments and the Sacraments)
If so, then do you not arrive at a community of Catholic Christians that is larger than the community of practicing Catholic Christians? And then, does Dionysius not speak of the same duality of boundary you do?
Everyone who holds the Catholic Faith is a Catholic Christian. Simply because one is not registered and attending Mass at a parish, does not automatically unchurch someone. Think of the immigrants to this country. For many years, many Catholics lived alone and apart from the comunity of believers. They would of necessity baptize their own children, and celebrate marriage on their own, and avail themselves of a travelling priest should he happen their way. They were no less Catholic than Italians living in the shadow of St. Peter's.
It is a mistake to limit the Catholic Church to the people written down on the register at the local parish. The Catholic Church is the comunity of believers who hold the Catholic Faith, are baptized at least in desire, and obey the lawful pastors of the Church.
One does not need to practice the faith to be a Catholic either. We are all aware of people who are Catholic, but who only attend Mass infrequently if at all.
Additionally, it is clear that people such as the adherents to the Traditional Anglican Communion, who are requesting integration into the Church, are Catholic, even though not members proper. Similarly, the Eastern and Oriental Orthodox are Catholic by profession of faith, shared sacramental rites, obedience to lawful Bishops, and common identity. This is why we speak of our lack of full communion with them (an historical oddity only dating from 1729, when the Holy Office forbid it) as properly a matter between the Pope and their Bishops, where those two parties need to come to an understanding regarding the limits of power and authority in the Church held by various persons. If it were an issue between Latin and Eastern laity, Rome would never permit any exceptions to our having communion with them, receiving penance and extreme unction from them, etc.
OTOH, people who reject the Catholic Faith, or the authority of Bishops, baptized or not, are not Catholics, and are not in any way part of the Catholic Church.

"Similarly, the Eastern and Oriental Orthodox are Catholic by profession of faith, shared sacramental rites, obedience to lawful Bishops, and common identity. This is why we speak of our lack of full communion with them (an historical oddity only dating from 1729, when the Holy Office forbid it) as properly a matter between the Pope and their Bishops, where those two parties need to come to an understanding regarding the limits of power and authority in the Church held by various persons. If it were an issue between Latin and Eastern laity, Rome would never permit any exceptions to our having communion with them, receiving penance and extreme unction from them, etc."

Thanks for mentioning this as the concept of "communion" is often loosely applied down to the level of the laity. Communion is in fact a matter of relationships between and among bishops (or abbots) to whom we laity, monastics and lower clergy owe obedience. It is for that reason that issues of reunion and/or intercommunion in the sense of receiving the sacraments, must be resolved initially between and among the hierarchs even if as a matter of ecclesiology in the Eastern Church and as a matter of practicality in the Western Church, the laity, monastics and lower clergy will have to recognize and accept any reunion which may come about.

I see much to recommend the approach of the Latin Church to the question of intercommunion by economia under certain circumstances. On the other hand, the virtually universal rejection of that exercise of economia by the Orthodox hierarchs to me makes good sense as reception of the Eucharist is the ultimate symbol of a real unity which doesn't exist. This of course raises the question of why apparently an intercommunion with the Oriental Orthodox is allowed by a limited economia. As Kosta has pointed out, at least historically, the theological differences between the non Chalcedonian and Orthodox Churches are more profound than those between Orthodoxy and the Latin Church.

Final point on intercommunion. When that concept or economia was first proclaimed by Rome in the 1960s, it was made very clear that on a diocese by diocese basis this should only be allowed after consultation and agreement with the local Orthodox hierarch. In this country that was not done and it made for some bad feelings just as Rome predicted. I understand that at least some Latin Rite Ordinaries have consulted with their Orthodox counterparts and when told that Orthodoxy will not accept the idea, the little statements contained in most missalettes about intercommunion with the Orthodox have been removed. Unfortunately some priests and bishops, despite complaints from the Orthodox hierarchs, are still preaching this to the confusion of the laity and lower clergy. We've seen examples of it right here on FR with Roman Catholics who think that Orthodoxy and the Latin Church are "in communion".