I would suggest not. But, it’s not entirely clear. If Christ did indeed eat the bread and wine then He ate of His own Body, Blood, Soul, and Divinity. But let’s look close to see if He actually consumes the bread and wine.
There’s nothing in the Institution Narratives that suggests that He did.
It’s important, I think, to remember that the Last Supper happens in the context of a Passover celebration. This implies that Jesus
did, in fact, eat and drink – after all, He would have had to, or else He would not have participated validly in the Passover obligation! However, it leads us to an interesting question: does the passage’s narrative of eating (bread) and drinking (wine) occur in the actual context of Passover ritual, or does Christ
add to the evening by introducing additional ritual?
In Luke’s account, Jesus only drinks wine
before beginning the Passover meal. His distribution of the bread happens at an indeterminate time, and his distribution of the chalice happens “after they had eaten.”
Matthew and Mark place the distribution of both bread and wine “while they were eating.” Again, can we say that this is necessarily part of the Passover ritual? Or, isn’t it more reasonable to suggest that Jesus adds this to the ritual?
Mark adds Jesus’ comment about “not drinking again of the fruit of the vine”
after the distribution of the Precious Blood (recall that Luke places this comment
before the Institution of the Eucharist).
So, what can we conclude? IIRC, Scott Hahn’s “fourth cup” theology suggests that all of these references (to the drinking of wine, although I can’t recall whether this includes a discussion of the breaking of the bread) are part of the Passover ritual.
On the other hand, if we look simply at the face of the text, it would seem reasonable to suggest that it doesn’t tell us (at the very least, it doesn’t tell us
explicitly) that Jesus shares in the consumption of the Eucharist. On the other hand, He Himself
is the Passover sacrifice of the New Covenant, so it wouldn’t seem necessary (for the sake of the ritual) for Him to consume the sacrifice.