No. Paul is referring to the Judaizers who were telling people they had to keep the kosher laws of the OT in order to be joined to Christ.
What the Catholic Church means when it refers to Sacred Tradition is what Paul is talking about in these verses:
1Cor.11:2 I commend you because you remember me in everything and maintain the
traditions even as I have delivered them to you.
2Thes.2:15 So then, brethren, stand firm and hold to the
traditions which you were taught by us, either by word of mouth or by letter.
2Thes.3:6 Now we command you, brethren, in the name of our Lord Jesus Christ, that you keep away from any brother who is living in idleness and not in accord with the
tradition that you received from us.
Paul was referring to the oral teachings of the Apostles, himself included. The Bible is a large part of Sacred Tradition, but it was non-existant, as far as the NT is concerned, until the 4th Century. The Church Jesus established isn’t based on a book, but on the Apostles. Jesus gave his teachings to them and they passed on their teachings, orally and in written form to their successors. The Bible was compiled mainly for use in the liturgies of the Church–so everyone would be using the same books. A very good book whose text is online is:
Where We Got the Bible: Our Debt to the Catholic Church. Don’t let the title put you off. It’s very charitable towards Protestants, and it’s simple to read and understand.