No. Romans 8:7 is entirely consistent with Romans 7 being a description of the Jew under Torah. In Romans 8:6-8:
6The mind of sinful man[e] is death, but the mind controlled by the Spirit is life and peace; 7the sinful mind[f] is hostile to God. It does not submit to God's law, nor can it do so. 8Those controlled by the sinful nature cannot please God.
We obviously agree that this is describing the unbeliever. What does it say about the non-believer - that his state of mind leads to death and that the sinful mind cannot do good. These are precisely the same things that Paul says in Romans 7:
11For sin, seizing the opportunity afforded by the commandment, deceived me, and through the commandment put me to death
For I have the desire to do what is good, but I cannot carry it out.
Clearly the Christian does have the ability to carry out "good". So for that reason alone, we know Romans 7 is not characterising the Christian in any state.
But back to your objection: it is interesting that you gave only a snippet. Here is the
whole text about the man "delighting in the law of God":
22For in my inner being I delight in God's law; 23but I see another law at work in the members of my body, waging war against the law of my mind and making me a prisoner of the law of sin at work within my members
Paul is saying that the "mind that delights"
loses the battle to the law of sin. Paul's wording may be a tad confusing and I have some empathy for your point.
But Paul says so many things in Romans 7 that simply cannot be true of the Christian.