No, Paul had not yet gone to Arabia at that time.
"But when God, who set me apart from birth and called me by his grace, was pleased to reveal his Son in me so that I might preach him among the Gentiles, I did not consult any man, nor did I go up to Jerusalem to see those who were apostles before I was, but I went immediately into Arabia and later returned to Damascus" (Gal.1:15-17; NIV).
After Paul's encounter with the Lord on the Damascus road he went immediately to Damascus and not Arabia. And the verses which I quoted are a narrative of the events since he arrived in Damascus and do not show any trip to Arabia. That trip had to come later.
It appears to read as follows...
Acts 9:
8. And Saul arose from the earth; and when his eyes were opened, he saw no man: but they led him by the hand, and brought him into Damascus.
19. And when he had received meat, he was strengthened. Then was Saul certain days with the disciples which were at Damascus.
20. And straightway he preached Christ in the synagogues, that he is the Son of God.
Then you have the Galatians account - Galatians 1:
15. But when it pleased God, who separated me from my mother's womb, and called me by his grace,
16. To reveal his Son in me, that I might preach him among the heathen; immediately I conferred not with flesh and blood:
17. Neither went I up to Jerusalem to them which were apostles before me; but I went into Arabia, and returned again unto Damascus.
Verse 16 relates what Ananias was told by the Lord to relate to Paul, as Ananias was being used of the Lord as a witness before Israel and the Believing remnant not only of Paul's conversion, but of his having been sent to the Gentiles before Israel's due time conversion.
Acts 22:
10. And I said, What shall I do, LORD?
And the Lord said unto me, Arise, and go into Damascus; and
there it shall be told thee of all things which are appointed for thee to do.
11. And when I could not see for the glory of that light, being led by the hand of them that were with me,
I came into Damascus.
12. And one Ananias, a devout man according to the law,
having a good report of all the Jews which dwelt there,
13. Came unto me, and stood, and said unto me, Brother Saul, receive thy sight. And the same hour I looked up upon him.
14.
And he said, The God of our fathers hath chosen thee, that thou shouldest know his will, and see that Just One, and shouldest hear the voice of his mouth.
15.
For thou shalt be his witness unto all men of what thou hast seen and heard.
The details of verse 15, as to what Ananias related to Paul from the Lord?
Acts 9:
13. Then Ananias answered, Lord, I have heard by many of this man, how much evil he hath done to thy saints at Jerusalem:
14. And here he hath authority from the chief priests to bind all that call on thy name.
15.
But the Lord said unto him, Go thy way: for he is a chosen vessel unto me, to bear my name before the Gentiles, and kings, and the children of Israel:
16. For I will shew him how great things he must suffer for my name's sake.
Why Ananias?
Because he, being "a devout man according to the law,
having a good report of all the Jews which dwelt there," 22:12, was a perfect witness as a bridge of the change now afoot.
A change that would be suspect, as Acts records it was for a time. The means around this being a witness well known for being devout according to the law - Isaiah 8:
18. Behold, I and the children whom the LORD hath given me are for signs and for wonders in Israel from the LORD of hosts, which dwelleth in mount Zion.
19. And when they shall say unto you, Seek unto them that have familiar spirits, and unto wizards that peep, and that mutter: should not a people seek unto their God? for the living to the dead?
20. To the law and to the testimony: if they speak not according to this word, it is because there is no light in them.
Later, Barnabas would also be a witness of good report among all the Jews, whom the Lord would use as a witness of Paul's validity, Acts 4:36, 37; 9:26, 27.
In fact, whenever I deal with Messianics who assert Isaiah 8:20against Paul, the above are some of the examples I make use of.
But anyway, we have this, that appears to read as follows...
Acts 9:
8. And Saul arose from the earth; and when his eyes were opened, he saw no man: but they led him by the hand, and brought him into Damascus.
19. And when he had received meat, he was strengthened. Then was Saul certain days with the disciples which were at Damascus.
20. And straightway he preached Christ in the synagogues, that he is the Son of God.
Then you have the Galatians account - Galatians 1:
15. But when it pleased God, who separated me from my mother's womb, and called me by his grace,
16. To reveal his Son in me, that I might preach him among the heathen; immediately I conferred not with flesh and blood:
17. Neither went I up to Jerusalem to them which were apostles before me; but I went into Arabia, and returned again unto Damascus.
Together, in light of the above, they read as follows:
Acts 9:19
A. And when he had received meat, he was strengthened.
Paul has just found out the following from Ananias - Galatians 1:
15. ...pleased God, who separated me from my mother's womb, and called me by his grace,
16. To reveal his Son in me, that I might preach him among the heathen; immediately I conferred not with flesh and blood:
17. Neither went I up to Jerusalem to them which were apostles before me; but I went into Arabia, and returned again unto Damascus.
It is then - after his return from Arabia - that Acts 9:19 B comes in - "Then was Saul certain days with the disciples which were at Damascus.
20. And straightway he preached Christ in the synagogues, that he is the Son of God.
In short, he goes into Damascus in a state of shock for he has met face to face with the God of his fathers, in the person of God the Son: Jesus of Nazareth.
Remember the shock of 911 on the world?
Well, here was Paul's - Acts 9:11
And the Lord said unto him, Arise, and go into the street which is called Straight, and enquire in the house of Judas for one called Saul, of Tarsus: for, behold, he prayeth,
Shock being that sate where a total re-orientation often begins.
In Damascus, now all ears - literally! - he is informed by Ananias ...The God of our fathers hath chosen thee, that thou shouldest know his will, and see that Just One, and shouldest hear the voice of his mouth. Acts 22:14.
The details of which are... Acts 9:15's..."he is a chosen vessel unto me, to bear my name before the Gentiles, and kings, and the children of Israel:
16. For I will shew him how great things he must suffer for my name's sake.
Which Paul summarizes in Galatians 1 as:
15. But when it pleased God, who separated me from my mother's womb, and called me by his grace,
16. To reveal his Son in me, that I might preach him among the heathen; immediately I conferred not with flesh and blood:
17. Neither went I up to Jerusalem to them which were apostles before me; but I went into Arabia,
and returned again unto Damascus.
And Acts relates - Acts 9: 19B...Then was Saul certain days with the
disciples which were at Damascus.
20. And straightway he preached Christ in the synagogues, that he is the Son of God.
In short, in Arabia, he learns directly from the God of his fathers, just as Moses had centuries before him.
What does he learn?
Galatians 4:
25. For this Agar is mount Sinai in Arabia, and answereth to Jerusalem which now is, and is in bondage with her children.
26. But Jerusalem which is above is free, which is the mother of us all.
2 Corinthians 3:
14. ...their minds were blinded: for until this day remaineth the same vail untaken away in the reading of the old testament; which vail is done away in Christ.
15. ...even unto this day, when Moses is read, the vail is upon their heart.
Thus, he is preaching to the Jew first that Jesus is the Son of Christ, knowing full well that Jerusalem has been concluded in bondage with her children.
The intent of this "to the Jew first" being two-fold - that he "might save some" even as Israel is "diminishing away" to its status before God now as just another heathen nation, but also, as a continuing witness against their own, witness against themselves in their continuing resistance of the Holy Spirit speaking to them now, through Paul, Acts 13; Romans 9-11.
As he later
reminded the Thessalonians of Acts 17 - to whom he had also preached that "Jesus is very Christ..."
1 Thessalonians 2:
13. For this cause also thank we God without ceasing, because, when ye received the word of God which ye heard of us, ye received it not as the word of men, but as it is in truth, the word of
God, which effectually worketh also in you that believe.
14. For ye, brethren, became followers of the churches of God which in Judaea are in Christ Jesus: for ye also have suffered like things of your own countrymen, even as they have of the Jews:
15. Who both killed the Lord Jesus, and their own prophets, and have persecuted us; and they please not God, and are contrary to all men:
16. Forbidding us to speak to the Gentiles that they might be saved, to fill up their sins alway: for the wrath is come upon them to the uttermost.
That's what; the first or second epistle he wrote not to long after his having first met them Mid-Acts.
Read both 1 and 2 Thessalonians - see all that Paul is
merely reminding them of as to what he had preached and taught unto them - Romans / Ephesians truth through and through.