Let me have a go at this... 
Case,
This person is a non Christian who have never heard of Gospel or
what Church teachings is like.
He turns to prayer, not even God.
He wasn't converted and still is a 'free thinker'
This means most likely this person do not know God, never heard of
Christ, never heard of his teaching. as a 'free thinker', he most
likely do not believe in any god as well (maybe I am wrong in
this).
So, is Faith involved? maybe, though I don't think his faith is in
Christ/God and thus not surprising he remain not converted and
remain as a 'free thinker'.
I am not disputing that Christ/God is involed here, just that this
person may not realised it.
(btw, coincidentally, this happened to me before, never heard of
Gospel or what Church teachings is like till I was 14)