"Conversion" has two meanings. One is change of religion or denomination, e.g a Baptist becoming Catholic. The other is a change of the heart, multiple times described in the Gospel. It is a turn ("conversio" means turning) away from sin and toward Christ, sometimes instantaneous or rapid, sometimes very gradual. Such spiritual conversion may happen, and in fact should happen, to someone already baptized and churched. Ideally, a Christian is in a state of perpetual conversion as long as he lives.
Indeed.