Let me put it another way ...
Roman Catholic theologians define The Church as “a body of men united together by the profession of the same Christian Faith, and by participation in the same sacraments, under the governance of lawful pastors, more especially of the Roman Pontiff, the sole vicar of Christ on earth.”
If I do not place myself under the governance of the Roman Pontiff, does that disqualify me from being a member of the Christ’s Church (i.e., the communion of saints, the society founded by Our Lord Jesus Christ)?
If I do not place myself under the governance of the Roman Pontiff, does that disqualify me from being a member of the Christ’s Church (i.e., the communion of saints, the society founded by Our Lord Jesus Christ)?
UNDERSTAND THAT If you placed yourself "under the governance of the Roman Pontiff", and participated in the "profession of the same Christian Faith, and by participation in the same sacraments, BUT died with one mortal sin on your soul, you would not be saved.
Now, this "governance" needs further defining before we could say that you "disqualified from being a member of the Christ’s Church". If you outright reject the office of the pope,its authority, yes, you are outside of the Church and "disqualified" from being a member of the Christ’s Church".
Are you familiar with the SSPX? One could make the case that the SSPX are not "under the governance of lawful pastors, more especially of the Roman Pontiff", yet they LIVE their Catholic faith like few Catholics. They say they are united to ALL the popes, and owe their allegiance to the post Vatican II popes, but that they can not follow the current popes when they teach novelties (or ambigious teaching that appear to be novelties) never taught by the previous popes. In other words, they do not reject the office, the authority of the pope.
Venerable Pope Pius IX († 1878) recognised the danger that a pope could “teach contrary to the Catholic Faith”, and he instructed, “do not follow him.”
“If a future pope teaches anything contrary to the Catholic Faith, do not follow him.” (Letter to Bishop Brizen)
Theo, that is not the definition of the Church. That is something the Latins invented. The catholic Church is where the Eucharist is, and the Eucharist is where a bishop is; a bishop being someone who gets his authority in direct succession from the apostles.
Now, you may disagree with this, but this is what the catholic Church believed and professed as early as 105 AD (based on the epistles of St. Ignatius).
If I do not place myself under the governance of the Roman Pontiff, does that disqualify me from being a member of the Christ’s Church (i.e., the communion of saints, the society founded by Our Lord Jesus Christ)?
Theo, apparently you don't know much about the Church. Salvation is not in the Church. The Church is where you salvation is believed more likely to happen then going at it alone. Also, your concept of what salvation is has a great deal to do with where you look for it.
In the Eastern tradition of Christianity, salvation is not a juridical concept (justification), but one of restoration to the likeness of God (become Christ-like) which was lost by the Fall.
This restoration is made possible by grace, through repentance (permanent change) in one's thinking, and doing (theosis) in cooperation with the Holy Spirit, and following his lead. This effort is sustained though sacraments (spiritual food) which nourishes our spirit to persevere.
God can save anyone he wants, technically speaking, but one's chances are believed greatly enhanced by participating in the life of the Church, where out tendencies to stray are more likely to be corrected, for, as the Bible says, "narrow is the path."
none of the eastern Churches recognizes the Pope as the Vicar of Christ on earth, yet they are as catholic and as valid as the Latin Church because they all have bishops whose authority is based on apostolic succession, they all have valid sacraments, and valid priesthood.
Even Rome recognizes that Eastern Churches are 'real churches' even though the lack the fullness from not being ion communion with the Pope. And the Eastern churches say that the Latin Church lacks equally the fullness of being in communion with a significant number of her sister Churches. The Church is deficient in that it exists as two disunited "lungs," but the catholic Church exists in its fullness in any local church wherever a valid Eucharist is offered under a valid bishop.