You posted an excellent article by N.T. Wright! (Paul, Arabia and Elijah) I've always seen this period in Arabia as a time for meditation, maturity and preparation for Paul's upcoming ministry. I even linked this episode with Numbers, thus connecting Numbers and Galatians on the Bible Wheel. The Hebrew name of Numbers is "In the Wilderness" and in Galatians we find a lone reference to an apostle going alone to "the wilderness" (Arabia).
Now, with the clue that you bring up, the connection seems even stronger. Galatians links Arabia to Sinai. And according to Wright, Paul was like Phinehas and Elijah in reverse. Phinehas' story is recorded in Numbers, and Elijah's journey to Sinai is recorded in 1 Kings 19. The first links to Galatians because they share the same Spoke on the Wheel. As for 1 Kings 19, we know that Spokes 4 and 19 are atbash. Therefore, all the three "zealous" men are connected in the structure of Scripture.