Will the faithful eat and drink after resurrection?

Question

At Luke 22:17–18 (RSVCE) we read:

And he took a cup, and when he had given thanks he said, “Take this, and divide it among yourselves; for I tell you that from now on I shall not drink of the fruit of the vine until the kingdom of God comes.

We also read at Luke 24:42–43:

And while they still disbelieved for joy, and wondered, he said to them, “Have you anything here to eat?” They gave him a piece of broiled fish, and he took it and ate before them.

Do the above verses give any indication that we will, like the resurrected Christ did, have meals of communion after our own resurrection? What do the Catholic teachings say about carrying forward of mundane functions by the resurrected faithful in heaven?

Answer 1

There are two different things going in those passages in Luke

Those two narratives aren't necessarily pointing toward what happens in Heaven, as there are varying interpretations to what is meant by the arrival of the Kingdom of God. Since you asked for a Catholic viewpoint, and this topic comes up a lot during the RCIA ministry, here's an explanation that tries to put those two different chapters in Luke into context.

• TL;DR: per St Thomas Aquinas, those who reach Heaven won't need to eat

The Fourth Cup

The best answer I've heard on why Jesus didn't drink the fourth cup at the Last Supper was presented by Scott Hahn in The Fourth Cup. (The link is to a transcript of his 40 minute long talk on the Eucharist; I'd recommend the audio disc/tape if you can get your hands on it).
In summary: Jesus established the New Covenant and important signs thereof and linked it directly to the Old Covenant celebration (Passover). Part of the significance of Him not drinking the 4th cup is that we (the faithful) now drink the 4th cup each time we receive communion and drink the precious blood. That is a departure from the Jewish tradition that led up to that final supper. Before the faithful receive the precious blood, who drinks from the cup? The celebrant of the Mass. The celebrant, be he priest or bishop acts "in persona Christi¹" according to the Catholic teaching. This gets into the Catholic doctrine and practice of the Mass re-presenting (making it present again) key events in the Gospel, but one of the points that Hahn makes is that in this Sacrament the church also honors and fulfills the old covenant during the Mass.

Now what's the problem? The problem is that gospel account says something like this: after the third cup is drunk Jesus says, "I shall not drink again of the fruit of the vine until I am entering into the kingdom of God." And it says, "Then they sang the psalms."
Every Jew who knows the liturgy would expect: and then they went ahead and said the grace and the blessing and had the fourth cup which climaxed and consummated the Passover. But no, the gospel accounts say they sang the psalms and went out into the night. {snip} Why did he skip the fourth cup? After all, he was raised a Jew, he'd been celebrating the Passover every year of his life since he was a little boy according to the strictest laws of Moses.

Rather than seeing this as Jesus prefiguring a meal in Heaven, he is prefiguring how the Body of Christ (The Church) will complete the Passover meal. The extended explanation, by Hahn, ties together a lot of scripture in the Old and New Testaments.

Raised from the dead in His glorified body, not a spirit walking around

In Luke 24, you have two different experiences of the disciples after the Crucifixion. The first is the two walking to Emmaus who spoke with him and didn't realize it was Him until he broke the bread, and then vanished.

The second was a larger group of the disciples who saw Him in his glorified body. As you noted in that passage, He ate food. He was raised from the dead, and was not simply a spirit people were seeing. (Recall also "doubting Thomas" sticking his finger into Jesus wounded side and seeing the holes in his hands).

The importance of what he was doing has been covered by St Thomas Aquinas in the Summa Theologica (Part III, Q 54) regarding Jesus in his Glorified Body.

Of the seven properties of the glorified body identified by St. Thomas Aquinas, the first three are relevant for the purposes of this answer: (Summarized for brevity from here)

• Identity: The glorified body will possess its original identity in that it will be united to your soul. Your body will really be your body, but that does not mean it will look the same as it did during your life on this earth. When Jesus appeared to His disciples after His Resurrection, He often had to make Himself known in some way, even to those who were His closest disciples.

• Integrity: The glorified body will be integral (complete), regardless of how it was during its earthly life, or at the moment of its death, or after it has decomposed in the grave. ...All glorified bodies will be entirely integral.

• Quality: This is the property of the glorified body by which everyone in his glorified body will be as if in the prime of life.

Whether or not those in Heaven who leave their bodies behind eat and drink seems to be a different matter than what happens in our glorified bodies. If we are in our glorified bodies, then we can eat and drink. If we are purely in spirit in Heaven, before "the last day," we don't need to.

Saint Thomas Aquinas concludes that we will not eat in Heaven.

(Summa Theologica, Question 81)

Consequently those natural operations which are directed to cause or preserve the primary perfection of human nature will not be in the resurrection: such are the actions of the animal life in man, the action of the elements on one another, and the movement of the heavens; wherefore all these will cease at the resurrection. And since to eat, drink, sleep, beget, pertain to the animal life, being directed to the primary perfection of nature, it follows that they will not be in the resurrection.

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¹ In the person of Christ the Head

. . . CCC 1548 In the ecclesial service of the ordained minister, it is Christ himself who is present to his Church as Head of his Body, Shepherd of his flock, high priest of the redemptive sacrifice, Teacher of Truth. This is what the Church means by saying that the priest, by virtue of the sacrament of Holy Orders, acts in persona Christi Capitis:23

Answer 2

In line with the answer of @KorvinStarmast, early and medieval Christian theologians generally believed that that people in Heaven would not need to eat. Here is what Origen said in the third century:

Hence it happens that some people of the simpler sort cannot distinguish or discriminate between things that the divine Scriptures assign to the interior human being and those that they assign to the outer human being. They are deceived by the similarities of the terms, and they devote themselves to silly myths and empty fictions. Thus, for example, they believe that even after the resurrection corporeal foods will be necessary, and that drink will have to be derived not merely from that "true vine "(John 15:1) which lives forever, but also from vines and from fruit that grows on trees. But we shall see about these matters in another place.

This is from his commentary on the Song of Songs, as quoted in Richard Norris ed., The Song of Songs as Interpreted by Early Christian and Medieval Commentators (Eerdmans, 2003).