Yes, absolutely. Romans 6:17-18, 22 says,

But thanks be to God that though you were slaves of sin, you became obedient from the heart to that form of teaching to which you were committed, and having been freed from sin, you became slaves of righteousness. 
(22) But now having been freed from sin and enslaved to God, you derive your benefit, resulting in sanctification, and the outcome, eternal life.

and Romans 6:11-14 says,

Even so consider yourselves to be dead to sin, but alive to God in Christ Jesus. 
Therefore do not let sin reign in your mortal body so that you obey its lusts, 
and do not go on presenting the members of your body to sin as instruments of unrighteousness; but present yourselves to God as those alive from the dead, and your members as instruments of righteousness to God. 
For sin shall not be master over you, for you are not under law but under grace.
 
The power and penalty of sin is broken in the believer's life because of the death and resurrection of Christ and by the life of Christ in every believer through the Holy Spirit. The difficulty lies in the struggle we have with the flesh, which will be with us until we're in heaven. The flesh is still corrupt and still tries to get it's way. But we now have a choice to deny the flesh because we have a new nature in Christ, as we see in 2 Corinthians 5:17,

Therefore if anyone is in Christ, he is a new creature; the old things passed away; behold, new things have come.

and 2 Peter 1:4,

For by these He has granted to us His precious and magnificent promises, so that by them you may become partakers of the divine nature, having escaped the corruption that is in the world by lust.

Sometimes we get discouraged because the struggle with the flesh seems unending. But trust God and keep walking with Him and you'll see the Holy Spirit changing your life. Sometimes He delivers us from deep rooted weaknesses right away, and sometimes He chooses to do it over a longer period of time. But we trust Him that either way, God knows whats best for us, and if that's to struggle in a certain area, then we can be sure it's necessary for His work in our lives.