Valid Method Some Rabbis and Evangelical Protestant minister may indeed consider this a valid method (32 Rules of Rabbi Eliezer, as previously noted). But this type of Bible study is tenuous, often leading to false doctrines, and misunderstandings concerning the Bible teachings. This so often true when it comes to the study of Eschatology. Jumping around from one verse to another (esp. topically) without doing expository research, considering each context, is not a valid way to do in depth biblical research. And we should not be teaching new converts to do that type of Bible study at the very beginning of their discipleship.
Righteous Intent The use of the questionable method here is done with righteous intent, to be sure. And it has been effective in the saving of souls! (Along with many other methods) The ROMANS ROAD is a metaphor that is easily memorized. Whether evangelists who use it should be criticized, is a matter of concern. By all means same some, might be a legitimate motto.
Hermeneutical Method Having said that, a perfectly sound hermeneutical method for presenting the Gospel to inquiring souls would be to take the very first verse of the Road (3:23), and present it in context! Read the next verse as well (3:24). That type of exposition contains the "Full Gospel" sufficient for salvation!
This righteousness from God comes through faith in Jesus Christ to all who believe. There is no difference. For all have sinned and fall short of the Glory of God, AND are justified freely by his grace through the redemption that came by Christ Jesus. (Romans 3:22-24)
Not Just Word Order When translating often, the new verbage does not follow the word order of the original because of different syntax rules in different countries. No problem.
But here in this question, we are dealing with the new order of whole verses from different chapters...and that is a different ball game! That practice is suspect. Paraphrasing within a sentence, is legitimate in some cases (translating for children, etc.) But this does not underscore real hermeneutical research, either. Nothing takes the place of expository (hermeneutically contextual) treatment of the Scriptures. New convert should be grounded in this type of Bible study.