Only if interpreted through the lens of the doctrine of Apostolic Succession, which as an evangelical I do not hold. II Timothy 3:16-17 does not proscribe or prescribe extra-scriptural sources of doctrine, it simply addresses the value of scripture to the believer. Here lies the chasm between the Catholic and the Protestant and Reformed church.
Only if interpreted through the lens of the doctrine of Apostolic Succession, which as an evangelical I do not hold.
Well, I, and all Catholics, do interpret it that way. That's Tradition with a capital T.
The entire 2 Timothy teaches the importance of oral tradition, -- "the things which thou hast heard of me by many witnesses, the same commend to faithful men who shall be fit to teach others also" (2 Timothy 2:2). Desdemona did not restrict her post #25 to verses 15-16. 2 Timothy 3:15-16 taken in isolation indeed does not prescribe extra-scriptural sources, because it prescribed them in Verse 14: "But continue thou in those things which thou hast learned and which have been committed to thee. Knowing of whom thou hast learned them". These are the things talked about in Chapter 2, -- knowledge taught orally, and powers "committed" through the laying of hands.
Now, what is the "all scripture" of Verse 16? Verse 15 says, it is what Timothy learned from his infancy. That is the Old Testament -- most if not all of the New Testament was not written at the time Timothy, now an adult, was a child, and, of course, none of the New Testament was canonized in St. Paul's or Timothy's lifetime. If 2 Timothy 3:16-17 is to be taken as an argument for sufficiency of scripture, it would disqualify, at the very least, latter Epistles and the Revelation.