That would seem to be the way J. Gresham Machen thought about the relationship between forensic righteousness and the fruit of faith.
Of course [Jesus] died to produce a moral effect upon man. If He did not die, man would have continued to lead a life of sin; but as it is, those for whom He died cease to lead a life of sin and begin to lead a life of holiness. They do not lead that life of holiness perfectly in this world, but they will most certainly lead it in the world to come, and it was in order that they might lead that life of holiness that Christ died for them. No man for whom Christ died continues to live in sin as he lived before. All who receive the benefits of the Cross of Christ turn from sin unto righteousness. In holding that that is the case, the substitutionary view of the atonement is quite in accord with the moral influence theory and with the governmental theory. . . .
The true moral influence of the Cross of Christ really comes, in other words, only when we see that the moral influence theory regarding it is false; it comes only when we see that on the Cross Christ truly bore the penalty of our sins and buried it forever in the depths of the sea. He loves little to whom little is forgiven. If the sin for which we are forgiven is merely the light, easily forgiven thing that the advocates of the moral influence theory of the atonement think it is, then no great spring of gratitude with well up in our souls toward Him who has caused us to be forgiven; but if it is the profound and deadly thing that the advocates of the substitutionary view of the atonement think it is, then all our lives will be one song of gratitude to Him who loved us and gave Himself for us upon the accursed tree. (“The Bible and the Cross,” in God Transcendent, 183, 185)