Can a believer still choose to live a carnal, fleshly life after being set free?
Yes. Even as a believer, one retains free will after being set free, so it is possible for a Christian to choose carnal, fleshly living instead of being led by the Spirit. The admonition is to keep old Adam in subjection, but God does not force that choice.
Les explains that the word "reckon" in verse 11 means to come to a mental conclusion. The believer has freedom, but it is left with free will, requiring a decision even as a believer: will they live spirit-filled lives or carnal, fleshly lives? Les says yes, it is possible for a Christian to make that choice. The admonition is to be led of the Spirit, live profitable lives, honor the God of glory, and keep old Adam in subjection. God has not taken away the believer's free will. Les then points to the next verse, "Let not," showing that L-E-T implies choice, not force. A believer is left with the choice of not letting old Adam continue to reign in the mortal body. Many unhappy believers are miserable because old Adam is still controlling them, and they are the ones left with the choice.