Yes and yes, of course… unless they have no priest with them, in which case the answer is no and yes.
The jest is taken from the comments to this post at JimmyAkin.org. (Jimmy Akin is probably best known as a knowledgeable and entertaining apologist on the radio show Catholic Answers.) A questioner asks:
My wife and I have been debating the hypothetical situation of a space ship of Catholic colonists crashed and stranded on a far-distant planet, with no possibility of return to Earth or communication with Earth. And all the bishops and priests and deacons aboard have been killed in the crash.
Can they acclaim a new bishop and continue the Apostolic Succession, and have sacraments? She says no way. I suspect they could.
Jimmy says no, too, to the question of ordaining a new bishop, which (if you ask me) is the obvious answer.
I once brought up this exact same hypothetical in a conversation with a Lutheran friend when we were discussing the differences between the Catholic sacrament of Holy Orders and ordination of ministers in her own faith. I don’t remember exactly how it went — she had to get back to me after asking her dad, a Lutheran minister himself — but she was pretty sure that in her particular tradition, it was possible for the faithful to elevate a minister from among the community, who would then be able to effect the eucharist as they understand it (consubstantiation, in case you’ve forgotten).
On the surface, it appears to be a great disadvantage to our faith that there’s no way to generate a bishop, or a priest for that matter, in an isolated system of Catholics that doesn’t already possess a bishop- or priest-generator — i.e. a validly ordained bishop. Especially since, without a priest, there’s no ability to confect the Eucharist — so that extremely important sacrament is forever lost to such an isolated system of Catholics, unless they happen to have brought some consecrated hosts with them. (And in that case, I suspect the best disposition for such hosts is in Adoration. Maybe Viaticum if the entire community faces certain death.)
But it also serves as a good thought-experiment to show the essential quality of the Christian priesthood and episcopate as we understand it, the quality of being (literally) handed down from man to man from the apostles. It is what it is, and even the gravest necessity cannot change it.
Yet it’s not actually "the gravest necessity." Of the seven sacraments, only five — sacramental absolution, Eucharist, holy orders, anointing of the sick, and confirmation — require a priest or bishop to confer them. The sacraments which are the means of making new Christians, marriage and baptism, do not require a priest. So a Christian community can indeed sustain itself, and provide the means of salvation, to all generations, even if it has no priest and no possibility of obtaining or producing one. Neither confirmation nor the Eucharist is thought to be absolutely essential to salvation, in that no one is thought to be lost simply because he never had access to those sacraments (refusing them when he did have access is another matter). Nor is sacramental absolution; it’s one means that God gave us for forgiveness of our sins, and it’s the ordinary means, but it’s not the only means. Presumably God forgives whomever He wants.
Jimmy’s post also contains an excerpt from a remarkable story about Christians driven underground in Japan during the persecutions of the 17th-19th centuries.
(It’s worth noting that my Lutheran friend who was certain that the community could elevate a minister from among themselves, became less certain in the case that the community contained no males. In the Missouri Synod, the ministry is barred to women. So it turned out that she agreed, that there were certain things that couldn’t be changed about it even in case of apparent necessity…)
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