I am a Roman Catholic, and I have had some interaction with the Catholic Charismatic Renewal, but I am far from an expert on this movement
I can say that the Catholic Church is amillennial
we believe the 1,000 year reign of Jesus to be what we are in right now, with Jesus reigning through His Church
we believe that verses talking about people being called up into the sky, that this Rapture is the Final Judgment for all people, not some event that depopulates the earth of Christians before the Second Coming but is rather something that happens at the same time as the Second Coming
before Jesus returns, there will be a Great Apostasy, many people will leave Christianity and follow the final AntiChrist (also called the Beast or the Man of Lawlessness)
the antichrist is also described as a spirit and that all who deny that Christ came in the flesh are antichrists
we can take this to mean that every worldly system that seeks to reject God and replace God with man
so the secular humanism of the French Revolution and Soviet Russia were in the spirit of Anti-Christ and Robespierre and Lenin were antichrists in their own way
but near the end, a human being will come along who cooperates more fully with this demonic spirit then any 3rd world warlord or pagan Caesar ever has
many intelectuals in mainline Protestantism have rejected this teaching, so many American Catholics have chosen to ignore it
or they have been confused by Evangelicals and Baptists who say the Pope is the antichrist, so they just ignore the topic all together
but if you read books from 70 years ago or longer, you will see the belief that a single human individual will raise up as antichrist before the last days was very common within the Catholic Church