Sorry, that doesn't fit. Note the context: in verses 13 and 14 James states that God is taking from the Gentiles a people for himself. Next he states that the words of the prophets are in agreement with what is happening. (that God is taking from the Gentiles a people for himself.) And then he quotes Amos 9:11,12. In others words, James is stating that the Gentiles coming to Christ are a fulfillment of Amos 9:11,12.
Acts 15:14-17 is not a promise for some future date, but the very fulfillment of an Old Testament promise. You see, friend, the mystery unfolded in the New Testament was that the Gentiles were to be heirs together with Israel of the Old Testament promises. See Ephesians 2:11 - 3:13. Nothing could be stated plainer than that.
He who has ears, let him hear.