I've mentioned the Covenant with Adam both in sermon and blog posts recently, but I know that raises questions for some. First, is it proper to use the word covenant to describe Adam's relationship with God when the Bible doesn't use that term till Genesis 6:18 in reference to Noah? Second, was the covenant a covenant of works or of grace?
On the first question, I am convinced there are good reasons to view Adam's relationship with God in covenantal terms, though the word is not specifically used. The absence of the word 'covenant' certainly shouldn't bother us to much - many of my friends believe in a 'rapture' though the word doesn't appear anywhere in the Bible, and many more of us (all I hope) believe in the Trinity, though the word doesn't appear. What is more important is whether or not the elements of a covenant appear in the descriptions of God's relationship to Adam (in other words, if it quacks like a duck, and walks like a duck, it's probably a duck).
Are the important elements of a biblical covenant present in Adam's relationship with God as described in the early chapters of Genesis? Berkhoff summarizes, "two parties are named, a condition is laid down, a promise of reward for obedience is clearly implied, and a penalty for transgression is threatened"(Berkhof, Systematic Theology, pg. 213). Wayne Grudem concurs, "the essential parts of the covenant are all there—a clear definition of the parties involved, a legally binding set of provisions that stipulates the conditions of their relationship, the promise of blessings for obedience, and the condition for obtaining those blessings"(Grudem, Systematic Theology: An Introduction to Biblical Doctrine, pg. 516)
In addition, we shouldn't neglect the words of Hosea 6:7 which refer to Adam breaking covenant with God.
Finally, on the first question still, it seems nearly impossible to read Romans 5:14 without concluding Adam was in a covenant relationship with God (serving as covenant head). That's the point of connection Paul is trying to make - that's how Adam is a 'pattern of the one to come'. Apart from that similarity all Paul would be drawing upon is the dissimilarities between Adam and Christ. If only dissimilarities existed between Adam and Christ, on what basis does Paul refer to Adam as a 'type of the one who was to come'?
On the second question, whether or not it was a covenant of grace or works, the answer will depend on definitions and degrees of precision. The covenant was gracious in that Adam didn't merit the relationship. God graciously condescended to enter into this binding relationship with Adam. Berkhof says it well, "When God created man, He by that very fact established a natural relationship between Himself and man. It was a relationship like that between the potter and the clay, between an absolute sovereign and a subject devoid of any claim...From the very beginning, however, God revealed himself, not only as an absolute Sovereign and Lawgiver, but also as a loving Father, seeking the welfare and happiness of His dependent creature. He condescended to come down to the level of man, to reveal Himself as a Friend, and to enable man to improve his condition in the way of obedience. In addition to the natural relationship He, by a positive enactment, graciously established a covenant relationship" (Berkhof, pg. 215). So the relationship isn't one that Adam earned, but was graciously given to him. Moreover, the terms are gracious. Berkhof again, "When entering into covenant relations with men, it is always God who lays down the terms, and they are very gracious terms, so that He has, also from that point of view, a perfect right to expect that man will assent to them" (Berkhof, pf. 213). Another way of looking at: "Adam's obedience was a necessary condition but not the sufficient condition for life in God's favor...The sufficient condition for the covenant was the fatherly and kingly favor of God" (Williams, Far as the Curse if Found, pg 72).
So, on one hand, the covenant is rooted in God's graciousness. However, on the other hand, the conditions of the covenant are works based, not grace based. There is an 'if...then' quality to the covenant - 'if you obey, you will enjoy the blessing of life'. The terms of the covenant were clearly works based/obedience based, not graced based. In addition, using the term 'grace' to refer to this covenant lacks doctrinal precision (in my humble opinion). Grace isn't just kindness (or graciousness). Nor is it simply love. The covenant was clearly loving (there is often a false dichotomy presented between 'law' and 'love'. That false dichotomy should be torn down! God's law is his loving provision for man.) The covenant with Adam was also gracious and kind. However, I don't think it's proper to say it was a covenant of grace. Why? Before Adam's sin, there was not demerit. Grace and mercy are terms the Bible seems to use solely in relation to demerit. We don't get the punishment we deserve because of hour sin - that's mercy. We get gifts from God despite our positive demerit, our sinfulness - that's grace. Adam had no demerit, thence, no need for grace or mercy (before the fall, obviously).
Moreover, in the initial covenant agreement between Adam and God there were no provisions for grace if Adam failed. There were no sacrifices to atone for the sin of Adam if he failed. When he did, it required God to initiate an different covenant - a covenant based on grace. In essence, this new grace covenant "is simply the execution of the original agreement by Christ as our Surety...He came to do what Adam failed to do, and did it in virtue of a covenant agreement" (Berkhof, pg. 214).
I agree with Horton's assessment, "This account provides the soil for a robust notion of the humanity of Christ...Our Savior had to be the second Adam...On the basis of his having fulfilled the covenant of creation [his term for the covenant with Adam] representatively, he can now dispense his reward to us within a covenant of grace" (Horton, God of Promise, pg. 94). I have only come into my 'Covenant Theology' in the past three or four years, and am growing in a deep appreciation for it's merits, it's simplicity (as opposed to, say, dispensationalism), and it's potential for fruit in my study of the Word.
If you are interested in pursuing more on Covenant Theology, I'd recommend two books (great, though they have slightly different spins):
1. God of Promise: Introducing Covenant Theology, by Michael Horton
2. Far As The Curse Is Found: The Covenant Story Of Redemption, Michael Williams
Also, Berkhof has a lot to say about covenants in his Systematic Theology.