No - you have turned the Scriptures upside down! The Bible teaches when we respond to the Gospel, when we receive Christ, when we believe - THEN He regenerates us. That is seen CLEARLY in the following passages:

John 1:12-13 But as many as received him, to them gave he power to become the sons of God, even to them that believe on his name: Which were born, not of blood, nor of the will of the flesh, nor of the will of man, but of God.

1 Peter 1:23-25 Being born again, not of corruptible seed, but of incorruptible, by the word of God, which liveth and abideth for ever. For all flesh is as grass, and all the glory of man as the flower of grass. The grass withereth, and the flower thereof falleth away: But the word of the Lord endureth for ever. And this is the word which by the gospel is preached unto you.

Ephesians 1:13-14 In whom ye also trusted, after that ye heard the word of truth, the gospel of your salvation: in whom also after that ye believed, ye were sealed with that holy Spirit of promise, Which is the earnest of our inheritance until the redemption of the purchased possession, unto the praise of his glory.

First comes our response to the truth, then comes regeneration - being born again.