I would go further and say with St. Gregory Palamas that theosis is next to impossible without the Sacraments, especially the Eucharist. This is the whole point of the Sacraments, and especially the Eucharist.
I know that the Orthodox express no opinion on the possibility of "salvation" outside the Church, say for Hindus, saying simply that we do not know. Am I correct in saying the Roman Church now holds this opinion, or is the official teaching still no salvation outside the Church?
The Roman Church considers that a settled dogma. But we would also say God does not condemn people who simply are not Christians, unless they purposefully reject the Church. So a person living off in non-Christian lands is not being thrown into hell for failure to become a Christian. The Tridentine Catechism notes a greater concern - the people who are not part of the Church do not have direct access to the ordinary channels of grace, which are the Sacraments, and that this leaves them in a precarious situation as regards their ability to avoid and repent of sin.
The dogma is truly aimed at those who leave the Church, not those who have never heard of it in pagan lands. This is certainly the thrust of Origen, St. Cyprian, Lactantius, and St. Augustine in their comments on it.
As to the possibility of the salvation of Hindus and the like, our official position is that faith in Christ, and love of Christ are the sine qua non of salvation, per St. John 17.3. We do not pretend to limit how God might reveal the mystery of redemption to those to whom the Gospel has never been preached, and we allow that they might have a Baptism by Desire should it please God to reveal Truth to them. However, we also say with St. Paul that it is very necessary for the Church to be missionary and bring the Gospel to these people who are so desirous of Truth among the pagans.
"How are they to call upon Him in whom they have not believed? But how are they to believe Him whom they have not heard? And how are they to head, if no one preaches? And how are men to preach unless they be sent? ... Faith depends on hearing, and hearing on the word of Christ." (Romans 10.14-15,17)
This is a bit OT but, I need to disagree with the above statement - the Council of Florence has plainly stated what the church teaches in no uncertain terms....How folks seem to think this applies only to Catholics I really do not know - unless we're talking novus ordo re-interpretations.
It firmly believes, professes and preaches that all those who are outside the catholic church, not only pagans but also Jews or heretics and schismatics, cannot share in eternal life and will go into the everlasting fire which was prepared for the devil and his angels, unless they are joined to the catholic church before the end of their lives; that the unity of the ecclesiastical body is of such importance that only for those who abide in it do the church's sacraments contribute to salvation and do fasts, almsgiving and other works of piety and practices of the Christian militia produce eternal rewards; and that nobody can be saved, no matter how much he has given away in alms and even if he has shed his blood in the name of Christ, unless he has persevered in the bosom and the unity of the catholic church. - Eccumenical Council of Florence 1438-1445
Gen 6:8 Noah who "found grace in the eys of the Lord."
There is even biblical evidence that the unbaptized can find grace.
I absolutely agree with your interpretation that "The dogma [no salvation outside the Church] is truly aimed at those who leave the Church."