Answer
I would agree with your assessment of this particular set of verses. However, Paul's broader argument in chapter 3 (in fact, in chapters 1-5) is that the reason the Jews aren't superior to Gentiles is that both Jews and Gentiles are equally shut up under sin, and both Jews and Gentiles are equally justified by the same means: faith in the risen Christ. The idea of universal and total depravity underlies Paul's point in Romans 3, and is at the heart of the issue in Romans 1-5. Therefore, it is reasonable to use these verses in their context to deduce the doctrine of total depravity.
Answer by Jacob Hale
Jacob Hale lives in Florence, AL, and describes himself as a born-again follower of Christ who feels called to be a preacher.