I, as a follower of Yeshua, am a spiritual Jew. I am also descended from physical Israel.
But I do not view myself as a Messianic Jew.
A Messianic Jew can live in Israel...I can't, at least not yet.
Yes this is what is meant in Rom 11 about the grafting in. Even the natural branches that have been broken of e.g. Hebrew (Jewish) people need to receive Yeshua's redemptive work and apply Yeshua's blood over their lives (Just like the 1st Passover) to be grafted back in. Halleluyah! this is what is meant their is neither Jew nor Greek etc. We are all one in and through Yeshua OUR Messiah. Only by His innocent blood and redemptive work in our hearts and not just an intellectual "saying the sinners prayer" but by doing and showing His works i.e. the Torah in our lives which shows a change in behavior and shows the fruits of the Holy Spirit in one's life and trust me this is a lifelong process.
This is what James means when he says, James 2:18 But someone will say, "You have faith, and I have works." Show me your faith without your works, and I will show you my faith by my works.
James followed the Torah the commandments of God these are the good works. The New Testament was not compiled for centuries after these things were written. They had no New Testament at the time of the writing of this letter.
Shalom