If his ignorance is invincible then it is possible for him to be saved by the baptism of desire.
The fact that Ben knows 1) the Church exists, 2) there is a pope and a hierarchy, 1 of whom he invited on his show, 3) the story of Jesus Christ, 4) the Church's stance that only good Catholics get to heaven, and 5) that the Church's stance on salvation is so unique that he wanted to ask about it...
All of this shows Ben's ignorance is NOT invincible in ANY degree. In fact, Ben's quite knowledgeable and therefore his rejection of the Faith (if he dies in his rejection) prevents his salvation, per Church teaching.