Hi,
No it doesn’t. That passage doesn’t mention the Church at all. “All scripture is inspired by God and can profitably be used for teaching, for refuting error, for guiding people’s lives and teaching them to be holy.” (2 Tim 3:16) Everything that that passage says about Scripture has been taught by the Catholic Church for over 2000 years.
Also, it is speaking of the Old Testament because the Catholic Church had not compiled the New Testament yet since it was still being written—nor had the Church yet determined what books were inspired and which were not.
Fr. Vincent Serpa, O.P.