Can those be saved who do not turn to God from their ungrateful and impenitent walk of life?

By no means. Scripture says that no unchaste person, idolater, adulterer, thief, greedy person, drunkard, slanderer, robber, or the like shall inherit the kingdom of God.

Proofs

• By no means. Scripture says that no unchaste person, idolater, adulterer, thief, greedy person, drunkard, slanderer, robber, or the like shall inherit the kingdom of God. (1 Corinthians 6:9–10; Galatians 5:19–21; Ephesians 5:5–6; 1 John 3:14)