No, our nature is still the same, and still drawn to sin. This is manifested by the fact that after Baptism we continue to sin. No one is made righteous and perfect (cf Heb 12:23); only in God's eyes, Who sees the intent of our hearts.
Your theory is that the replacement by the Holy Spirit is "incomplete" and there is a "remanant" of the old nature...it's up to us to work with God to live under grace and not in our nature.
I didn't realize you don't believe in regeneration. What do you do with verses like these? :
Ezek 36:26 : I will give you a new heart and put a new spirit in you; I will remove from you your heart of stone and give you a heart of flesh.
2 Cor 5:17 : Therefore, if anyone is in Christ, he is a new creation ; the old has gone, the new has come!