You ask if the Catholic Church is dependent on the conciliar church for it's existence. The answer is no; the article states the opposite. The conciliar church is dependent on the Catholic Church for it's existence. If you want to see how this is explained, read the article.

Actually, since it's unlikely that the article will be read, I'll quote from the relevant section of the article which explains or describes the idea. It's located a little less than halfway down the article, in the section titled, "Should we deduce two materially distinct churches: one Catholic and one conciliar?" It says that two conclusions can be drawn. I get the impression that each of the two conclusions need to be taken in an absolute sense. Here's part of that explanation:

".....Just as one can say (with a pinch of salt) that liberalism is a Catholic heresy, in the sense that it is born of the Catholic Church and only exists and develops by "feeding off" the Catholic Church, so one can say that the conciliar church is born of the corruption of the Catholic Church, and it cannot exist but by living off this corruption as a parasite lives depending on an organism, sucking of the substance of its host to construct its own substance. There is a sort of transfer of substance, I would dare say, from one to the other, in a metaphorical sense and not in a philosophical sense. To become conciliar, there is no need to separate oneself from the Catholic Church; it is sufficient to allow oneself to become corrupted by the conciliar poison and to let ones substance become absorbed by the conciliar parasite. It is sufficient to practice the Mass of this new religion and to adhere, formally or materially to the liberal ecuмenism which gives it its form.

On the other hand, the conciliar church does not necessarily coincide with the Catholic Church, neither in its leaders or its members The leaders of one are not necessarily the leaders of the other. The members of the first can, by heresy, cease to be members of the second, but not necessarily. The Catholic Church is the only true Church, the only Church founded by our Lord Jesus Christ. But this does not hinder the conciliar church from being a social reality; not only a section, but a counterfeit church, led by a sect of directors, a sect whose ideology or system is the form of the conciliar church, and which manoeuvres it towards its ends, with its relays and executors, formed of a large part of the hierarchy and faithful Catholics more or less conscious and consenting, to a diametrical overturning which it is trying to bring about. In this sense, Fr. Calmel, O.P., was able to speak of the "church of pirates;" this metaphor says it all."

Alexandria: 

Holli, I agree with you.

Thanks, Alex., but you might reconsider your agreement with me.  I've been told that I have low reading comprehension. So my points may be ill-founded, and anchored in faulty understanding and the inability to grasp the essential content of the study.   I mean, (gasp),  I have not even the sense to understand that the OP was, in great part, anyway, an essay, or whatever, prepared by Bp Tissier, not X.
So you might wish to go back and re-read the treatise, extracting all its precious nuggets, and deriving from them the value which X meant to impart.
After all, this is Bp. Tissier we're talking about.  Remember Bp. Tissier, that noble cleric, who, along with his compadre, Bp. de Galaretta, co-authored with Bp.Williamson, a letter of severe warning to then SG Fellay a few years back, warning the latter not to get too cozy with Rome.  This man's wisdom and theological credentials can not be dismissed.  We must, perhaps, immerse ourselves in the tedium of his arguments and get from them what we can, before the mind becomes so benumbed that it can't go on, or before our reading comprehension levels descend to such dangerous levels, that real progress in understanding comes to an absolute standstill.

Our Lady of LaSallete explained it well:  “The Church will be in eclipse.”  The True Church is like beautiful, centuries-old castle that has stood the test of time, weather and all manner of military assaults.  

The Conciliar Church (ie the Jєωιѕн 5th column) is like a construction company coming along and turning the castle into a restaurant/bar, by putting up cheap metal siding on the outside of the castle’s stone walls, and adding a wooden deck in the front, and remodeling the inside.  These cheap and superficial changes will not last long and try as they will, cannot hide the strength, history and imposing nature of the castle.  One day, the castle will return to its rightful orthodox owners and all these “modern improvements” will be taken down, and the castle will once again be seen and admired for its beauty.