Would Peter have gone to Caesarea without the supernatural vision and the Holy Spirit telling him to go?
No. Peter would not have gone to Caesarea without the supernatural vision, the men at the gate, and the Holy Spirit's voice commanding him. As a Jew, he viewed Gentiles as dogs and believed God could have nothing to do with them; only divine intervention overcame that.
Les teaches that Peter would never have gone to Caesarea apart from such a supernatural environment: the trance, the men at the gate, and the voice of the Holy Spirit speaking. He asks his classes, “Do you think Peter would have gone to Caesarea?” and answers, “No way. No way.” This is because, as far as Peter was concerned, Gentiles were still dogs, and God could have nothing to do with them. Les also reminds people that Peter was not a pig-headed Jew who should have known better; Peter was a Jew who knew what was expected and was acting in accord with the program thus far. God’s intricate timing had the men from Cornelius arrive at Simon’s gate just as Peter came through the vision, and the Holy Spirit told him to arise, go with them, doubting nothing, for I have sent them.
While Peter thought on the vision, the Spirit said unto him, Behold, three men seek thee.