Yes. Arabia is another name for Petra. After his conversion at Damascus, Jewish persecution became too severe and Paul fled to Arabia where he apparently remained for three years, later returning to Damascus and going on to Jerusalem, Galatians 1:15-18. It appears that during that time Damascus was under the control of King Aretas of Petra. Aretas along with the Jews tried to apprehend Paul, II Corinthians 11:32-33, Acts 9:23-25.