Uh, no. At the point in time that Paul wrote this, "scripture" referred ONLY to the "Old Testament". There was no "New Testament".
The OT certainly is "teaching, rebuking, correcting and training in righteousness".......but not for salvation, as Paul also taught exhaustively in many places (the OT is about "the Law (of Moses)"...the NT is about salvation)
The OT testifies about Jesus, Jesus *IS* salvation; therefore, the OT _is_ about salvation.
John 5:39 — “You study the Scriptures diligently because you think that in them you have eternal life. These are the very Scriptures that testify about me,”