Part of the theology of the Eucharist is basically in the same line of thinking of the theology if the Incarnation. If God can be alive on Earth as Jesus Christ while being nailed to a cross and dying, and he can still be Lord and ruler of the Universe, holding existence in place because he has the power to do many things as once - be many places at once - then he can certainly be in the Eucharist too. If he could not, then he could not have died on the cross without the universe falling into non-existence.
In all truth, even the Romans thought that Christians were cannibals (and incestuous, actually). Pliny the Younger was sent by emperor Trajan to observe their behavior, and witnessing the way they worshipped, confirmed that the words "Take and eat, this is my body, etc..." were used during the Eucharistic feast. The early Christians were accused of being cannibals because of this:
http://www.fordham.edu/HALSALL/ancient/christian-cannibals.html. The Romans had heard of what went on in Christian services - mainly only based off of the prayers used and not eye-witness accounts - and assumed cannabalistic behavior was in fact going on.