Yes, but not in so many words in Scripture. The Bible uses several terms/phrases to describe the "old man" of Romans 6:6, the person one is apart from God. The "old man" is carnal, that is, focused upon fleshly impulses and desires (Philippians 3:18-19); the fleshly-minded "old man" is "not subject to the law of God neither indeed can be," (Romans 8:7); the "old man" is temporally-oriented, largely ignoring eternity to come, investing in the here-and-now (see the Philippians quotation above); the "old man" is prideful, selfish, contentious and temperamental (Galatians 5:19-21; Titus 3:3). And so on. Paul wrote very dramatically about this "sin nature":
Romans 7:19-24
19 For the good that I want, I do not do, but I practice the very evil that I do not want.
20 But if I am doing the very thing I do not want, I am no longer the one doing it, but sin which dwells in me.
21 I find then the principle that evil is present in me, the one who wants to do good.
22 For I joyfully concur with the law of God in the inner man,
23 but I see a different law in the members of my body, waging war against the law of my mind and making me a prisoner of the law of sin which is in my members.
24 Wretched man that I am! Who will set me free from the body of this death?
Does the "sin nature" retain the power to compel me, a born-again believer, to sin? Absolutely not. Romans 6 dissolves this idea completely (see also: Colossians 2:10-13; Colossians 3:1-3; Galatians 2:20; Galatians 5:24; Galatians 6:14). I am as free of the power of the "old man," of my sin nature, as I choose to be. Wonderful news, is it not?