[QUOTE=flodnak]
Also, if the man chosen to be Pope is a layman, he must be free of any impediment to becoming a priest. The most obvious impediment is marriage, so he has to be a bachelor or a widower.
[/QUOTE]
This is gonna be an awkward statement. First, let me note that yes, I am Episcopalian (=Anglican in America), but I’ve always been fascinated by the organized complexus of minutiae that goes to make up Catholic doctrine and praxis.
That said, what follows is, TTBOMK, what the Catholic Church teaches-- not represented as my own beliefs, nor some objectively true definition of the world, but their own belief system, so far as I understand it.
That said, per ecclesiam catholicam it is not possible to ordain a woman priest or bishop. That is, you can go through the motions of doing so (illicitly, of course) but it will not be a valid action. On that metaphysical plane where priests are indelibly marked with the sign of their priesthood, the woman would remain unmarked. Even more so would this be true for the episcopacy and the higher levels of Catholic hierarchy. (The diaconate is specifically excluded from this discussion – the majority view of theologians is that the same thing applies as in an attempted ordination to the priesthood: not a valid action, while a minority of theologians think that Scriptural references to deaconesses mean that it’s possible, just not done. Present teaching of the Magisterium is that women may not be ordained deacons – as opposed to saying that they cannot, on which it has not as yet ruled AFAIK.)
Hence no woman can ever become Pope – because the Pope is first and foremost the chief bishop of the Church, and a woman cannot become a bishop.
Now, having gone through all that gyration to answer the “potential woman pope” question and in so doing to illustrate something Catholic doctrine considers an impossibility, turn to the married clergy question.
Clerical celibacy is a Law of the Church – and specifically of the Latin Rite. Eastern Rite married men can be and are regularly ordained; the Pope can dispense from the rule in the Latin Rite and on occasion does. The rule could be changed today if the Holy Spirit led the Pope to decide to do so, or if the bishops in General Council so voted. There have been married popes, starting with Peter (whose wife is never mentioned in the Bible, but whose mother-in-law is). There is even a case or two of legitimate father-and-son papacies, where both were elected pope at different times.
So being a married man would not be a bar to becoming Pope; the College of Cardinals would simply have to be led to the conclusion that this person is the right candidate for Pope anyway.