And add to that...
Does eating the eucharist impart salvation to the person?
Yes, or no will suffice.
The physical, material act alone? No. No more than sitting by a stereo playing a recording of the Holy Scriptures being read brings the faith that comes by hearing. So, neither are magic, there's more involved than the physical.
For the limited purposes of a quite limited explanation, you can think of the Holy Eucharist as a means of God's grace, and whatever questions you have about salvation and the Holy Eucharist, apply the term 'grace' instead.