Is the Covenant of Works Innate to Man?

The experience of every human being points to a remnant of the Moral Law's Covenant of Works (WLC 93 and WCF 4.2) written on the human heart; not just the moral sense of right and wrong but also of reward and punishment. 

Q. 93. What is the moral law? 

A. The moral law is the declaration of the will of God to mankind, directing and binding everyone to personal, perfect, and perpetual conformity and obedience thereunto, in the frame and disposition of the whole man, soul and body, and in performance of all those duties of holiness and righteousness which he oweth to God and man: promising life upon the fulfilling, and threatening death upon the breach of it.

WCF 4.2 -

2. After God had made all other creatures, he created man, male and female, with reasonable and immortal souls, endued with knowledge, righteousness, and true holiness, after his own image; having the law of God written in their hearts, and power to fulfill it: and yet under a possibility of transgressing, being left to the liberty of their own will, which was subject unto change. Beside this law written in their hearts, they received a command, not to eat of the tree of the knowledge of good and evil; which while they kept, they were happy in their communion with God, and had dominion over the creatures.

This innate covenant of works is revealed by the common experience of guilt everyone experiences upon getting caught doing something they know to be wrong and their effort to avoid blame. The subsequent attempt to self-justify in order to be declared in the right often follows. To escape a verdict of condemnation, to prove the worthiness of being in the right are as natural to man as breathing. They come to the surface between individuals with even the smallest of disagreements or offenses. Guilt, condemnation, measuring up to what is right and worthy of approval are interwoven parts of the human soul. If this is true, it stands to reason that this reality found in every human heart of Adam's posterity, i.e. to avoid punishment/rejection and win approval/acceptance, was woven by God into Adam's heart upon his creation. If this isn't the case and the Covenant of Works was only given to Adam as an external covenant in Genesis 2 after his creation, then how is it a part of every individual who follows after Adam? 

But the image of God in man principally consisted in his conformity to the moral perfections of God, or in the complete rectitude of his nature...

There was then no need that the moral law should be written on tables of stone, for it was engraved on the heart of man in fair and legible characters.

Shaw, Robert. The Reformed Faith, exposition on WCF 4

Even C.S. Lewis, an Anglican, alluded to this writing in The Problem of Pain,

 "All men alike stand contemned, not by alien [i.e. outside of himself]  codes of ethics, but by their own, and all men therefore are conscious of guilt."