Do the prophets agree that God would call out a people for His name from the Gentiles?
Yes. The prophets agree with Simeon's report that God at first visited the Gentiles to take out of them a people for His name. James cites Amos, showing that after this calling out, God will rebuild the tabernacle of David. So Gentiles are included in God's purpose.
Les explains that after Peter quieted the opposing Jews, James answered and recounted how Simeon declared God's first visit to the Gentiles to take out of them a people for His name. James then says the prophets agree, citing Amos: after this calling out, God will build again the fallen tabernacle of David and set up its ruins. Les concludes that yes, God will call out of the Gentiles a people for His name. He adds that Gentiles do not enter Israel's intimate "My people" relationship, which awaits Israel's complete belief at Christ's return; outside this Acts passage, Gentiles are more correctly referred to as His born ones.
And to this agree the words of the prophets; as it is written,