Albert Barnes on "God-Breathed"
In searching more on a possible allusion to Genesis 2:7 in 2 Timothy 3:16, I discovered that at least one commentary (and probably more if I were to look further) allows for this possibility, the New Testament Notes, by the American Calvinist theologian Albert Barnes (1798-1870), who has this to say about θεόπνευστος in 2 Timothy 3:16:
Is given by inspiration of God. All this is expressed in the original by one word -- Θεόπνευστος Theopneustos. This word occurs nowhere else in the New Testament. It properly means, God-inspired -- from Θεός Theos, God, and πνέω pneō, to breathe, to breathe out. The idea of breathing upon, or breathing into the soul, is that which the word naturally conveys. Thus God breathed into the nostrils of Adam the breath of life, Ge 2:7; and thus the Saviour breathed on his disciples, and said, "Receive ye the Holy Ghost," Joh 20:22. The idea seems to have been, that the life was in the breath, and that an intelligent spirit was communicated with the breath. The expression was used among the Greeks, and a similar one was employed by the Romans. Plutarch ed. B. ix, p. 683, 9. τους ονείρους τους θεοπνεύστους tous oneirous tous theopneustous [the inspired dreams]; Phocylid. 121. της δε θεοπνεύστου σοφίης λόγος εστιν αριστος tēs de theopnoustou sophiēs logos estin aristos [the word of inspired wisdom is excellent]. Perhaps, however, this is not an expression of Phocylides, but of the pseudo Phocylides. So it is understood by Bloomfield. Cicero, pro Arch., 8. poetam -- quasi divino quodam spiritu infiari. [a poet -- as if breathed upon by a certain divine spirit] The word does not occur in the Septuagint, but is found in Josephus, C. Ap. i. 7. "The Scriptures of the prophets who were taught according to the inspiration of God, κατα την επίπνοιαν την απο του Θεου kata tēn epipnoian tēn apo tou Theou [according to the inspiration of God]" In regard to the manner of inspiration, and to the various questions which have been started as to its nature, nothing can he learned from the use of this word. It asserts a fact -- that the Old Testament was composed under a Divine influence, which might be represented by breathing on one, and so imparting life. But the language must be figurative, for God does not breathe; though the fair inference is that those Scriptures are as much the production of God, or as much to be traced to him as life is. Comp. Mt 22:43; 2 Pe 1:21. The question as to the degree of inspiration, and whether it extends to the words of Scripture, and how far the sacred writers were left to the exercise of their own faculties, is foreign to the design of these notes. All that is necessary to be held is, that the sacred writers were kept from error on those subjects which were matters of their own observation, or which pertained to memory; and that there were truths imparted to them directly by the Spirit of God, which they never could have arrived at by the unaided exercise of their own minds. Comp. Intro. to Isaiah and Job.Barnes does not make a strong case for an allusion to Genesis 2:7 in 2 Timothy 3:16, but he offers more examples on "inspiration" for our consideration. He does offer an intriguing suggestion: "The idea seems to have been, that the life was in the breath, and that an intelligent spirit was communicated with the breath." The suggestion is intended to connect the two verses hermeneutically, life and intelligence being infused with the same breath given by God, but this depends upon an already established allusion to Genesis 2:7 in 2 Timothy 3:16, and that hasn't yet been shown.
Perhaps I'll try to check other commentaries . . .