I think I agree with what Antoni said. Yes, we are fallen. From the moment we are conceived. And there is no one who lives and does not sin - every day we add to our sins. If we repent, being in the Church, God's mercy heals us and sanctifies us. If we do not repent, we turn our back on God until eventually we experience his love as wrath. But I don't think converting means "invite Jesus into your heart", I think it means "turn away from sin in repentance and towards God" (constantly, every day, not just once)
The idea you're describing from GT is found in Lutheranism, but I'd say that what it actually means when a Lutheran says that is probably very different from what an Evangelical or the more Calvinist type would mean