No, the believing Jewswho lived in the first centurycalled on the name of the Lord Jesus so therefore, this epistle is addressed to them:
"Unto the church of God which is at Corinth, to them that are sanctified in Christ Jesus, called to be saints, with all that in every place call upon the name of Jesus Christ our Lord, both their's and our's" (1 Cor.1:2).
And here is what Paul told those who in every place call on the name of the Lord Jesus:
"For as the body is one, and hath many members, and all the members of that one body, being many, are one body: so also is Christ. For by one Spirit are we all baptized into one body, whether we be Jews or Gentiles, whether we be bond or free; and have been all made to drink into one Spirit" (1 Cor.12:13).
Cornelius Stam, the founder of the Berean Bible Society, wrote the following commentary on 1 Corinthians 1:2:
"There are other evidences that the kingdom saints of Paul's day became members of the Body of Christ. In I Corinthians 1:2, Paul addresses his letter to the Corinthian church, 'with all that in every place call upon the name of Jesus Christ our Lord, both theirs [those in every place] and ours [those with Paul].' And he says to 'all' these believers 'in every place': 'For by one Spirit are we all baptized into one Body, whether we be Jews or Gentiles' (I Cor. 12:13). How can this be made to exclude the Judean believers?" (Cornelius Stam, Commentary on Galatians [Stevens Point, WI: Worzalla Publishing Co., 1998], 198).