II. The question is not whether natural theology (which is such by act as soon as a man is born, as the act of life in one living or of sense in one perceiving as soon as he breathes) may be granted. For it is certain that no actual knowledge is born with us and that, in this respect, man is like a smooth tablet (tabulae rasae). Rather the question is whether such can be granted at least with regard to principle and potency; or whether such a natural faculty implanted in man may be granted as well as put forth its strength of its own accord, and spontaneously in all adults endowed with reason, which embraces not only the capability of understanding, but also the natural first principles of knowledge from which conclusions both theoretical and practical are deduced (which we maintain).
III. The question is not whether this knowledge is perfect and saving (for we confess that after the entrance of sin it was so much obscured as to be rendered altogether insufficient for salvation), but only whether any knowledge of God remains in man sufficient to lead him to believe that God exists and must be religiously worshipped [sic].
V. We find in man a natural law written upon each one's conscience excusing and accusing them in good and bad actions, which therefore necessarily implies the knowledge of God, the legislator, by whose authority it binds men to obedience and proposes rewards or punishments. ...
[Francis Turretin, Institutes of Elenctic Theology, 1. III. 2-3, 5]
Francis Turretin was the last of the great Reformed Scholastics, and the last leader of the Reformation in early modern Geneva, Switzerland. His Institutes of Elenctic Theology bears the fruit of much Reformed thought over the many years since the Reformation, and should be required reading for all pastors and theologians who consider themselves Reformed.
In his Institutes, which I am slowly going through, Turretin has an interesting take on "natural theology." It seems that for Turretin, "natural theology" corresponds to what we would today call "General Revelation." The knowledge of God available to everyone informing them of God's existence and the basics of His moral law is ubiquitous to all. All men have this revelation. Even the suppression of the truths of General Revelation does not negate that fact, because they must be actively suppressed, for what can be known about God IS plain to them, for God has made it plain to them (Rom. 1:19).
Such truths however do not make up any form of natural theology, which is the idea that Man can come up with a true coherent theology of God purely from the truths of Nature. There is a gap between knowing there is a God and knowing some of His moral laws, and being able to produce a partial but correct doctrine of God from Nature. This gap is the gap between cognitive coherent and intuitive inchoate knowledge. The former I deny to General Revelation while affirming the latter. I would like to note here that any theology of General Revelation produced by Christians always appeal to axioms that make sense only within a Christian theistic framework. That is why I will gladly affirm General Revelation while denying Natural Theology, because I just do not see how one can derive a coherent albeit partial doctrine of God from Nature alone apart from Scripture and its framework.
Do Turretin and the Reformed scholastics endorse Natural Theology? They certainly use the phrase "natural theology" positively, but, as I have shown, Turretin uses it only in the sense of General Revelation. While I certainly cannot rule out the possibility of any of them endorsing Natural Theology, I do not see Turretin doing so in this particular instance. I am therefore not convinced that Turretin or any of the Reformed Scholastics would have approved of Natural Theology, and any argument to that effect needs to not just appeal to the approval of the phrase "natural theology," since it is rather clear that Turretin means by that phrase something different from how the term is used today.