It is the Church Militant's job to preach the Gospel, God as always does the conversion and salvation.
Yes, of course, but Church Militant saves souls by fulfilling Christ’s order to evangelize. We are His hands, feet, and mouths on Earth. That was Wikipedia’s definition of Church Militant, which is the traditional definition.
The more recent Catechism of the Catholic Church touches on it here:
http://www.scborromeo.org/ccc/p123a9p5.htm
PM me if you want to talk about it further.