Yes, these are words used by us as well. And it is my understanding that the partaking of bread and wine is symbolic of this.
However, I would think, again from my limited time as an EO, that it is Grace we hope for and the mystical communion with Christ. Everything centers around theosis, and communing is one of the ways we get help with that.
And finally, for us, the Eucharist is a way to become united spiritually with not only Christ, but also the other church members present. The sobornost .
These are just my understandings and I welcome correction from others with stronger understanding than my own.
That's not to say we don't want Russia to remain primarily Orthodox, of course. :-)