Were the Gentiles included in Israel's covenant promises while God was dealing with Israel from Genesis 12 to Acts 9?

No. Paul writes Gentiles were not in the covenant promises and were not citizens of Israel. While God dealt with Israel on the basis of covenants—from Genesis 12 until Acts 9—the Gentile was outside. Jesus did not take the Greeks because He could not be their faith's object until He died, was buried, and rose.

Les teaches that while God was dealing with Israel on the basis of the covenants, from Genesis 12 until Acts 9, the Gentiles were outside. Paul, under the inspiration of the Spirit, said Gentile believers were not in the covenant promises and were not citizens of the nation of Israel. Jesus did not take the Greeks because He could not be the object of their faith until He had died the death of the cross, been buried, and risen from the dead. Les also illustrates this Gentile exclusion with Jonah, who did not want to go to Gentile Nineveh, and with Peter in Acts 10 when the Lord told him to go to Cornelius.

When were the Gentiles outside God's covenant promises and not citizens of Israel?

Paul, writing under the inspiration of the Spirit, said Gentiles were not in the covenant promises and were not citizens of the nation of Israel. This was the case from Genesis 12 until Acts chapter 9, while God was dealing with Israel on the basis of the covenants. The Gentile was outside.