Jesus appears to reveal his betrayer “He that dippeth his hand”. (Matt 26:23)
Jesus pronounces woe unto his betrayer. (Matt 26:24)
Judas asks if it is him. (Matt 26:25a)
He said unto him, Thou hast said. (Matt 26:20-25)
Jesus confirms it is Judas. (Matt 26:25b)
The Lord’s Supper is given. (Matt:26-28)
Jesus explains this will be his last meal. (Matt 26:29)
Matthew does not say Judas left.

Mark’s Version (Mark 14:17-25)
Judas is at the Meal. (Mark 14:17)
Jesus says someone will betray him. (Mark 14:18)
The disciples wonder who the betrayer is. (Mark 14:19)
Jesus appears to reveal his betrayer, “the one… who dippeth with me”.(Mark 14:20)
Jesus pronounces woe unto his betrayer. (Mark 14:21)
The Lord’s Supper is given. (Mark 14:22-24)
Jesus explains this will be his last meal. (Mark 14:25)
Mark does not say Judas left.

Luke’s Version (Luke 22:14-20)
Judas is at the Meal. (Luke 22:14)
Jesus desires to eat the Passover before he suffers. (Luke 22:15)
Jesus explains this will be his last meal. (Luke22:16)
The Lord’s Supper is given. (Luke 22:17-20)
Jesus appears to reveal his betrayer “But, behold, the hand of him.” (Luke 22:21)
Jesus pronounces woe unto his betrayer. (Luke 22:22)
The disciples wonder who the betrayer is. (Luke 22:23)
Luke does not say Judas left.

John’s Version
John suggests this all happened near the end of supper. (John 13:2)
Jesus knows he is going to die. (John 13:3)
Jesus washes his disciple’s feet. (John 13:4-9)
Jesus hints they are not all clean. (13:10)
It is explained what Jesus meant in verse 10. (John 13:11)
Jesus explains the washing of the feet. (John 13:12-17)
Jesus explains that the scriptures teach that the Messiah will be betrayed. (John 13:18)
Jesus explains why he brought up the scripture. (John13:19)
Jesus explains his connection to the Father. (John13:20)
Jesus declares one of them will betray him. (John13:21)
The disciples wonder who the betrayer is. (John 13:22)
Peter and John ask who the betrayer is. (John 13:23-25)
Jesus reveals the betrayer as Judas. He “dipped the sop, he gave it to Judas Iscariot” (John 13:26)
Jesus asks Judas to do it quickly. (John 13:27)
The disciples did not fully know what Jesus was saying to Judas. (John 13:28-29)
After receiving that “Sop” Judas left. (John 13:30)
After Judas leaves, Jesus says, “Now is the Son of man glorified,” (John 13:30)
John does not talk about the Giving of the Last Supper.

Conclusion
Based on all four accounts, I would conclude that Judas Iscariot did not partake in the Eucharist. My conclusion is based mainly on these points.

1. John records that these events happened near the end of the meal.
2. In all four Gospels record Judas was revealed as the betrayer with the dipping of the “Sop.”
3. The three Synoptic Gospels record what was said during the Eucharist.
4. Matthew and Mark record that Judas was revealed before the Eucharist was given.
5. John records that right after the dipping of the “Sop” Judas left.
6. Matthew, Mark, and John all seem to agree Judas was revealed as the traitor before the Eucharist.
7. Luke appears to be the only one who records the event out of order. (maybe; see Luke’s Note).

The Four Gospels Version:

Judas is at the Meal. (Matt 26:20, Mark 14:17, Luke 22:14)
Jesus desires to eat the Passover before he suffers. (Luke 22:15)
This all happened near the end of supper. (John 13:2)
Jesus knows he is going to die. (John 13:3)
Jesus washes his disciple’s feet. (John 13:4-9)
Jesus hints they are not all clean. (13:10)
It is explained what Jesus meant in verse 10. (John 13:11)
Jesus explains the washing of the feet. (John 13:12-17)
Jesus explains that the scriptures teach that the Messiah will be betrayed. (John 13:18)
Jesus explains why he brought up the scripture. (John13:19)
Jesus explains his connection to the Father. (John13:20)
Jesus declares one of them will betray him. (Matt 26:21, Mark 14:18, John13:21)
The disciples wonder who the betrayer is. (Matt 26:22, Mark 14:19, Luke 22:23, John 13:22)
Peter and John ask who the betrayer is. (John 13:23-25)
Jesus reveals the betrayer as Judas. (Matt 26:23, Mark 14:20, Luke 22:21, John 13:26)
Jesus pronounces woe unto his betrayer. (Matt 26:24, Mark 14:21, Luke 22:22)
Judas asks if it is him. (Matt 26:25a)
Jesus confirms it is Judas. (Matt 26:25b)
Jesus asks Judas to do it quickly. (John 13:27)
The disciples did not fully know what Jesus was saying to Judas. (John 13:28-29)
After receiving that “Sop” Judas left. (John 13:30)
After Judas leaves, Jesus says, “Now is the Son of man glorified” (John 13:30)
The Lord’s Supper is given. (Matt:26-28, Mark 14:22-24, Luke 22:17-20)
Jesus explains this will be his last meal. (Matt 26:29, Mark 14:25, Luke 22:16)

Luke’s Note:
Luke’s account appears to be the most out of order. But I do not think it is out of order. I do admit this is weak, but I think the key to understanding Luke’s account comes in the word “But” found at the beginning of verse 21 (Luke 22:21). In most translations, the word “But” is accounted as something Jesus said. I believe it is a narrator’s “BUT,” meaning that Luke was saying this happened “BUT” before this Jesus said this.

This is complete conjecture; Luke is could have been writing on something like a scroll. When you make a mistake, there is no delete button. Luke could have been writing and realized he forgot to add a part and used the narrator’s “BUT” to explain that something happened before.