A conscience is a carnal way of referring to the Holy Spirit, more specifically it means that their heart has not been hardened towards the conviction of the Holy Spirit, which is awesome.
There is a point when we can disconnect so far from the Lord through our behavior, that we no longer hear the Holy Spirit. The desire to be forgiven is a testament to the heart of the person, who receives the correction. In short, the answer to the spirit of this question is yes.