We Catholics DO think something like the “fullness” of the Church “subsists”among those in communion with the Holy See.
But, while we loosely speak of “converts” the technically precise name for the act of a baptized person's “becoming a Catholic” is “being received into full communion.” It is quite wrong to say they ‘converted.’
If one can entertain the idea, “lex orandi lex credendi” then a good place to go for an experiential understanding of what we think would be the “solemn collects” of the Good Friday Liturgy.
In them, as I like to say it, we pray that God will, so to speak “apply” the benefits of the Cross to all the world. So we pray for Catholics, for all Christians, for Jews, for theists, and for atheists, that grace will be shed on them.
When I think of “the Church” in the broadest sense, I think of everyone we pray for on Good Friday.
In other words Catholics believe you have to be a Catholic to be saved but you also pray for all the heathens and hope they join the Catholic Church so they can become saved. Gee thanks.
Feeney was disciplined for claiming that only formal members of the Church could be saved. The idea that only formal members of the Catholic Church could be saved was a misrepresentation of Extra Ecclesiam Nulla Salus and is not the teaching of the Church. The Church teaches that those who die in a state of sanctifying grace go to heaven. The question then becomes, how do those who are not formal members of the Church by sacramental baptism obtain sanctifying grace initially or if it has been lost by mortal sin.
Remember, the Church teaches that any baptism by water in the Name of the Father, Son, and Holy Spirit is a valid sacramental baptism, makes one a member of the Church, and confers sanctifying grace and is cause for the remission of Original Sin and personal sin.
The Church also teaches baptism by desire and baptism by blood. It is by an elastic interpretation of baptism by desire that many ecumenical types have claimed that there might be salvation outside the Church.