No, 2 Tim 3:16 doesn't support calling the NT God-breathed.
All Scripture (πᾶσα γραφὴ)
Better, every Scripture, that is, every passage of Scripture. Scripture as a whole is as αἱ γραφαί or αἱ γραφαί ἅγιαι. Ἱερά is never used with γραφὴ. Γραφὴ is the single passage, usually defined by this, or that, or the, or which saith.
Is given by inspiration of God (θεόπνευστος)
N.T.o. olxx. From θεὸς God and πνεῖν to breathe.
God-breathed. The word tells us nothing of the peculiar character or limits of inspiration beyond the fact that it proceeds from God. In construction omit is, and rend. as attributive of γραφὴ every divinely-inspired Scripture.
And is profitable (καὶ ὠφέλιμος)
According to A.V., καὶ and is merely the copula between two predicates of γραφὴ. It is divinely inspired and is profitable. According to the interpretation given above, καὶ has the force of also. Every divinely-inspired Scripture is, besides being so inspired and for that reason, also profitable, etc. Ὡφέλιμος profitable, Pasto. See on 1Ti_4:8.
For doctrine (πρὸς διδασκαλίαν)
Better, teaching. Comp. to make thee wise, 2Ti_3:15.
Reproof (ἐλεγμόν)
Better, conviction. N.T.o. oClass. Comparatively frequent in lxx, mostly in the sense of rebuke: sometimes curse, punishment. See Ps. of Solomon 10:1, but the reading is disputed with ἐλέγχῳ. See on the verb ἐλέγχειν, Joh_3:20.
Correction (ἐπανόρθωσιν)
N.T.o. Twice in lxx. Restoring to an upright state (ὀρθός erect); setting right.
Instruction (παιδείαν)
Better, chastisement or discipline. See on Eph_6:4. In lxx mostly correction or discipline, sometimes admonition. Specially of God's chastisement by means of sorrow and evil.
Vincent.
2Ti 3:16 All πᾶσα Scripture [is] γραφὴ
God-breathed θεόπνευστος and καὶ is useful ὠφέλιμος for πρὸς instruction, διδασκαλίαν, for πρὸς conviction, ἐλεγμόν, for πρὸς correction, ἐπανόρθωσιν, [and] for πρὸς training παιδείαν in ἐν - τὴν righteousness, δικαιοσύνῃ,
Yes it does.
J.