Yes. A born-again believer who does not live for Christ will still go to heaven, as the context of 1 Corinthians 6:9-11 makes clear in verse 12:

"Or do you not know that the unrighteous will not inherit the kingdom of God? Do not be deceived; neither fornicators, nor idolaters, nor adulterers, nor effeminate, nor homosexuals,

10 nor thieves, nor the covetous, nor drunkards, nor revilers, nor swindlers, will inherit the kingdom of God.

11 Such were some of you; but you were washed, but you were sanctified, but you were justified in the name of the Lord Jesus Christ and in the Spirit of our God.

12 All things are lawful for me, but not all things are profitable. All things are lawful for me, but I will not be mastered by anything."

Paul makes a distinction between the unrighteous who will not inherit the kingdom of God and the Christian when he says "and such WERE some of you". He's making the point that Christians should not live like those who are not of God's household. In verse 12, he says this is not PROFITABLE for the Christian.

However, Christians who live in sin will suffer loss, even though they are saved from hell; as  1 Cor 3:13-15 says,

"each man's work will become evident; for the day will show it because it is to be revealed with fire, and the fire itself will test the quality of each man's work.

14 If any man's work which he has built on it remains, he will receive a reward.

15 If any man's work is burned up, he will suffer loss; but he himself will be saved, yet so as through fire."