Remember there is no such thing as a nature/grace dichotomy. Nature is grace, and grace, rooted as it is in the very nature of God, is entirely natural.
When we come to this table, we are certainly partaking of Christ. But we are not doing this because the table is a different kind of event, dispensing grace, over against all the other kinds of events we go through (nature).
All nature, all creation is covenantal. This table is at the center of that covenant reality, but it is not a different kind of thing. It is not that mystical spiritual things happen here that do not happen elsewhere. Everywhere we go, all day long, in everything we do, we are partaking covenantally. When we come to this table, this does not change—although it does intensify.
This is simply another way of saying that there is nothing magical about this Table. But do not draw the wrong conclusions from this. The whole world is magical, the whole world is suffused with the glory of God, and the whole creation invites us to fellowship with Him.
Because God has sovereignly allowed creatures to disobey Him, those who do so reject His company, and reject His fellowship. But they do not thereby escape the necessity of partaking. They are covenant creatures, living in a covenant world. They can no more reject the universal presence of covenant realities than they can escape the universal presence of gravitation.
So the choice is this. Commune with the Lord here, and in everything else you do, and the blessing of God in Christ rests upon you, and upon all your endeavors. Reject Christ here (either by refusing to come, or by coming unrepentantly), and you are partaking elsewhere, in covenant fellowship with the world, the flesh, and the devil. But you belong to Christ. Come to Him now. Come in faith, He welcomes you.
So come, and welcome, to Jesus Christ.