To be Christian is to be a follower of Christ and His Disciple. Partly people can in some truth be apart of His Body. In a disconnected reality. In a disconnected way. But they are not incorporated into His Body.
If you bear someone’s last name, but were adopted. You could deduce you were not incorporated through the reality of the two (man and woman) becoming one flesh. But adopted by them.
But then again, what about Saint Joseph? He did not receive the Body, Blood, Soul, and Divinity in the Eucharist, of Christ. Yet, he did receive Him as his Son, by what way? Adoption!
How does that reconcile?
Because, when you eat and drink the body and blood, you are becoming Christ-like. Or Persona Christie. Thus, when people speak to you, welcome you. They are receiving Christ by-proxy.
But if they reject you for the Eucharist? Then know they rejected Him in the same manner and way.
Thus, do they reject Christ. And even then there’s ignorance. For Christ, in the manner of rejection said Crucified: “Father, forgive them. They know not what they do.” Thus, it is still possible for them to receive Christ by all that He taught and did for Salvation.
Thus, yes, it is necessary for the Eucharist to be not just part of the His Body, but in His Body. As incorporated into His Presence. And accepting even that by-proxy of the Church. Even the avenue of Scripture can by-proxy be the reception of Christ. In so far as the soul accepts Him as He stood on earth. And everything He said, taught, and did. Which means the Eucharist.
Someone could be dying, come to realize this. And didn’t have time to go through the Rites of Initiation. Is he lost? No! Because, as Christ said to His Father to forgive them. Remember, us finite human beings, slow witted, and less like being child-like as we get older. Thus, finding it hard to accept what Christ said, taught, and did to fullest sense.
To answer your question further. Is the Sacrament of the Eucharist necessary to be a part of the Body of Christ? Yes. But it works in many channels and extraordinary ways as Christ’s own life represents through the Gospel. A channel, a doorway of Hope. It is just the acceptance of the Eucharist people must accept. Which means subjecting one’s pride in humility to the Humility of God’s Presence in the Holy Eucharist.