I agree with you that the television coverage of the papal obsequies has given the American public a crash course on the Catholic Church, and I would include in the definition of "public" Catholics born in the last 40 years who don't remember the Latin Mass (I was an altar boy before and after the Second Vatican Council) or the impression, common in 1950s America, that Roman Catholicism was an exotic, insular, even "foreign" religion.
For some Protestant TV reporters, that information gap persisted into the 1970s. I remember the TV news star who, a short time into one of the papal funerals in 1978, declared in his omniscient way that "the service ends as it began, with splendid ceremony" only to be corrected by the resident Vatican hand who knew that the Mass had only just begun!
My guess is that some of the traditions surrounding the death of the pope and the election of a new one will seem as strange to Generation X and Y Catholics as they will to Protestants—like something out of The Da Vinci Code. The accessibility, informality, and media savviness of John Paul II, at least in the early days of his papacy, are in some ways an awkward fit with the rituals associated with his passing.
For example, the cardinals will vote for a "supreme pontiff," but the last two popes were invested, not crowned, an innovation of John Paul I, who preferred to be known as "supreme pastor." John Paul II was able to promote order, orthodoxy, and evangelism—as you well put it—within this less-triumphalist ethos. Although many young Catholics may not realize this, the "pope hat" worn by John Paul I and John Paul II was the miter worn by all bishops, not the triple tiara with its overtones of worldly power that survives on the papal coat of arms.
The saintliness of a pope is not determined by his headgear, of course, but it will still be interesting to see if the next pope forgoes the tiara and a "coronation."