Question about pilgrimages/traveling monk

In my book, a young monk from a monastery in the late medieval times goes on a long journey where he meets the main character. I need him to be on the road for a long time. My plan was to have the abbot send him on a sort of pilgrimage to find his way back to God, maybe because he has been questioning his faith and is not acting right (he’s an orphan grown up there). Would it make sense for him to not just have ONE destination goal for a pilgrimage, but rather that he’s riding around the country, visiting different relics etc, kind of avoiding to return since he still feels like he hasn’t found what he was looking for on the journey (his faith? purpose ?) It is fantasy, so it does not need to be 100% accurate, but I still want it to somehow make sense.