Μὴ γένοιτο! No way! Gentiles don’t need to be included in Israel. In fact, the opposite is true; we Gentiles are saved by faith in Christ without being included in Israel. That’s one of the apostle Paul’s big points in Romans and Galatians.
We are, of course, included in the promises given to Abraham (Rom 4:11, 16; Gal 3:7). But being a child of Abraham is not the same as being a member of Israel. That’s why Paul says that Abraham is the Father of many nations (Rom 4:17-18), not that Abraham is the father of one nation, Israel, that has somehow been redefined or expanded to include other nations. Jewish Christians and Gentile Christians are united, not in Israel, but in the promises to Abraham and ultimately in Christ.
The idea that the Gentiles are included in Israel is one of the (if not the) fundamental exegetical mistakes of the New Perspective on Paul.
PS that’s probably why Paul almost always speaks of the church using familial terms, such as “children” and “sons”, rather than political terms (i.e. as a “people”, which is a political word).
Gadenz, Pablo T. Called from the Jews and from the Gentiles: Pauline Ecclesiology in Romans 9–11. Edited by Jörg Frey, WUNT II.267. Tübingen: Mohr Siebeck, 2009, esp. page 82.