Whenever someone from the Protestant faith reads up on the history of Christianity, By reading the writings of the Church Fathers, As well as the Holy Bible, They clearly see that their protestant churches are wrong in their claims regarding Catholicism. They usually either convert to Catholicism or to Orthodoxy. By contrast, It is naive Catholics that end up going for Protestantism, & becoming extremely bigoted to their former Catholic faith.
Martin Luther King was initially a Catholic until he read the Bible, Which the Catholics believed in, Yet they inhibited his ability to read it. When he read it he realized that the Catholics were misinterpreting the Bible the entire time. He knew that something in the Catholic lifestyle wasn't right so he did his research, And instead of following everything else he was willing to contradict every thing he believed in so he could know the truth. So to wrap it up, I believe that actually well formed Catholics become Christian, But I do not believe that poorly formed protestants become Catholic.
Protestantism is distinctive from Catholicism in our affirmation of Sola Fide, And Sola Scriptura. Since there is no basis whatsoever to the claims of the authority of the Catholic church, No one should see it as an authority. Catholic apologists often cherry-pick among "church fathers" to get claims that somewhat sound like their doctrines. The truth is these "church fathers" often lived hundreds of years after the time of Jesus and know the scriptures no more than we do, So there is no reason to take anything they say as inerrant. And, Even if we do go to them for the sake of argument, They don't consider the bishop of Rome to have any special authority until much later. Therefore, There is no unbroken succession of Popes starting with Peter. Even Peter wasn't a pope himself.