Did the Gospels ever predict that God would turn to the Gentiles and form a body of Christ?
No. The Gospels contain no prediction that God would turn to the Gentiles and call out from them a body of Christ made up of Jew and Gentile. The Old Testament prophetic timeline looked only to Christ's suffering, death, resurrection, God's wrath, and the coming Kingdom.
Les explains that from Abraham until Christ's first advent, God was primarily dealing with the nation of Israel. Christ's earthly ministry was to Israel, and they crucified Him. After His ascension, the Old Testament prophetic program pointed next to the wrath of God, the tribulation, and then the Kingdom. What was missing was the church age. Les notes there is not a word in the Old Testament about the church age, and not a word in the Gospels that God would turn to the Gentiles and call out of them a body of Christ of Jew and Gentile. The Old Testament only looked forward to Christ coming, suffering, dying, being raised, then God's wrath, then the Kingdom. Peter, for example, had no concept beyond that Old Testament timeline.