There is no way to conclude that from I Cor 10:16, especially when it is read in context:
"Wherefore, my dearly beloved, flee from idolatry. I speak as to wise men; judge ye what I say. The cup of blessing which we bless, is it not the communion of the blood of Christ? The bread which we break, is it not the communion of the body of Christ? For we being many are one bread, and one body: for we are all partakers of that one bread. Behold Israel after the flesh: are not they which eat of the sacrifices partakers of the altar? What say I then? that the idol is any thing, or that which is offered in sacrifice to idols is any thing? But I say, that the things which the Gentiles sacrifice, they sacrifice to devils, and not to God: and I would not that ye should have fellowship with devils. Ye cannot drink the cup of the Lord, and the cup of devils: ye cannot be partakers of the Lord's table, and of the table of devils."
In this verse the "body" referred to is partaking of the "bread" -- and that "body" is the membership of the church, hence the word "communion" or fellowship rather than "eucharist". It appears that pagans had a type of communion service as well and Paul is telling those of the body of Christ [the Church] to stay away from it.
Just a few chapters later +Paul talking about the body of Christ as one body of which we are made members by the Spirit. So I'm thinking that separating out the koinonia part as something radically distinct from the body of Christ is also not really taking the entire trend of Paul's discourse into account.
Yeah, I know that's vague ...
Yes, Paul completely destroys your position here, because he draws an analogy from the Christian Eucharist to the sacrifices of pagans to their idols. He is saying that Eucharist is to Christians what pagans' sacrifices are to pagans, that is, that it is a true sacrifice in which Christians share (koinonia) the Body and Blood of Christ.