You have explained RCIA very well from a personal point of view. Thank you!
**Many conversions happen literally at the hour of death.**
My priest has talked about numerous Sacraments, Anointing of the Sick, Baptism, Holy Eucharist, Confirmation (the priest is authorized in these cases to perform this Sacrament.)
He even talked about performing a valid marriage for the couple (one partner dying, of course.) It seems that even the Sacrament of Reconciliation was mentioned by him too, depending on if the person is coming back to the church — revert, as you say above.
The answer is simple: indeed, if one cannot physically get a priest, yet has a spiritual need -- such as a desire to convert, or be baptised, or confess a sin, -- God will count his desire and supply the effect of the sacrament based on his sincere prayer alone. What will happen is what happened to the Good Thief on the cross: his repentance, his good works in defence of the innocently accused Christ, his desire to be with Christ in Heaven all counted as a sacrament, that lead him to heaven.
On the other hand, when there is no physical impediment to asking the Church for sacramental conversion, it would be a sign of a confused mind and a weak faith not to follow through in the ordinary way.
This doctrine can be summarized thus: the sacraments are necessary under "necessity of suitableness", but not absolutely. See Sacraments.