When I was in college, I was involved in Baptist Student Union, I attended a few meetings of the Newman Society (a Catholic group), and ... I forget the name of the other group, it was a long time ago, but it was a Pentecostal group. Oh, and I attended one or two meetings of a forth but they weren't very active, so I migrated over to the Baptist group.
I'd say all of them functioned much like a lay-led Bible study slash Christian social club. They each had a lay leader who would present some sort of Bible study or message at each meeting. And they'd have social activities. Mostly they were intended to give Christian students an opportunity to meet with other Christians, learn a little about spiritual things, and have some refuge from secular culture.
None of the groups I was involved with was particularly evangelistic. I'm sure that a non-Christian who came seeking answers to spiritual questions would have been welcomed. I don't recall any activities specifically aimed to convert non-Christians. There are probably campus Christian groups out there that are seriously working to bring in converts, but that wasn't really the primary purpose of the groups I was with.
I recall the Newmans bringing in a priest to conduct a mass on at least one occasion. I don't recall if that was a regular thing or a special case. So I guess they had some respect for the clergy; there was certainly no indication that they saw their own leaders as an alternative to the clergy. Protestants don't have the same view of the clergy that Catholics do, so I don't recall anyone even talking about it in Protestant groups.
AS to converting Catholics to Protestantism ... I'm sure any Protestant group would welcome a Catholic who wanted to convert. And they'd see that as a good and positive thing. I mean, doesn't everybody figure that his group is better than any competing group? If he thought some other group was better, he'd join them. But I never ran into any campus Protestant group that saw it as their mission to convert Catholics.