But can't this passage be Paul talking as someone under the law who then realizes the saving grace of Christ? When he says "thanks be to God," he speaks as the one who realizes the salvation of Christ.
No ma'am, it cannot. The phrase, right after "Thanks be to God, through Jesus Christ our (in other words, 'my') master.
The reason that Paul is saying 'Thanks' to His present tense Master (Lord) Jesus Christ, is that "Ara" ('Therefore': a conclusive particle) he serves the law of sin with His flesh, but the Law of God with his mind. Understanding that the word "Mind" used throughout this passage, is the Greek word "nous", which refers to your will, further clarifies this.
Although Paul's flesh has sinful urges, his will serves the Law of God. This is WHY he says "Thanks be to Jesus Christ my Master".
7because the mind set on the flesh is hostile toward God; for it does not subject itself to the law of God, for it is not even able to do so,
This verse says that the unregenerate man cannot subject himself to the law of God, not that the unregenerate man cannot "serve the law of God."
Jesus even commended the Pharisees at one point and holds them up. I'm in a hurry now and will have to look that up later.
Serve from Chapter 7...
douleuō
Thayer Definition:
1) to be a slave, serve, do service
"Submit to" from Chapter 8...
hupotassō
Thayer Definition:
1) to arrange under, to subordinate
2) to subject, put in subjection
These words are listed as synonyms. The mind of the carnal, unsaved man, CANNOT submit his mind to the Law of God. Paul says He, while serving sin with his flesh, has a mind that is submitted to and serving the Law of God.
Paul is writing in Chapter 7, referring to his experience as a saved man, present tense, while he is writing scripture.