Yes; however this does not necessarily mean that we will use that power, although we should.
Entire sanctification is a second benefit (2 Corinthians 1:15, 1 Thessalonians 5:23-24).
Salvation is indeed still given to many who are not yet circumcised of heart (Romans 2:25-29, Romans 4:11); who do not keep (the spirit of) the law perfectly, having not been wholly sanctified yet. But if they are not progressing towards a deeper and more perfect walk; or at the very least maintaining their current walk (see Philippians 3:16), it ought to be questioned as to whether they are in fact truly born again.
First off, thank you, especially, for Philippians 3:16. I've been looking for that scripture on and off for a long time.
Now regarding your first sentence. Maybe we will know that it was wrong to sin when we've been empowered not to when Jesus says to us, ‘I never knew you; depart from Me, you who practice lawlessness!’
Even though we who have the Spirit to follow and are not under the law, the principle is the same as in Romans 2:
12 For as many as have sinned without law will also perish without law, and as many as have sinned in the law will be judged by the law 13 (for not the hearers of the law
are just in the sight of God, but the doers of the law will be justified; 14 for when Gentiles, who do not have the law, by nature do the things in the law, these, although not having the law, are a law to themselves,
Therefore, if we have been empowered to not sin, and go ahead and willfully sin anyway, why should we be surprised if we wind up having our names being blotted out of the Book of Life? Besides, the apostles have given us plenty of warnings to not sin.