The weakness of that approach is that Paul's rhetoric has been designed so carefully that people fail to recognize the rhetoric that is there. Even Ben Witherington III, having written on Romans and also on New Testament rhetoric, has failed to recognize that rhetoric in Romans-- of augmentation in 5:16-19. Paul also repeats "God gave them up" in 24-28, which has the effect of reinforcing the desperate situation of the Jews (despite the issue briefly sounding more like gentile behavior). It took several years for me to stumble upon the message of Rom 6 and 7 and it was just recently that 2:17-3:2 made sense in the context. Therefore, a read-through of the letter, while a great idea, is not going to give a sufficient starting point to understand the letter intuitively -- if that is even possible by anyone. The letter is more like Isaiah in that the ideas have to be worked through. The verses have to be studied deeply. I have written over 60 pages to explain Paul's approach in Rom 4:1-2 -- partly because I was getting more insight into the indirect rebuke Paul was making.One thing I am recommending for the first session is to "hear" the letter in full. There are several ways to do this but a simple (and free) approach is to use the Blue Letter Bible online system that has an audio reading of the text. It runs about an hour and a quarter for the whole letter.
Romans Chapter 1
English Standard Version: Romans Chapter 1 @ Blue Letter Biblewww.blueletterbible.org
P.S. -- I'm just hoping people will catch on to the situation Paul was confronting in Rome and how he worked it through his writing to fix problems of the gentiles and ultimately get them to accept that Jews could be saved.