Maybe. That's really the best we can get. Our earliest witness to the Jesus story is Paul. Paul does mention the the crucifixion and the events leading up to it a couple of time, such as in Romans 8:32 and 1 Cor. 11:23. In Romans, Paul states that God did not spare his son but handed him over. In 1 Cor., Paul states that on the night in which Jesus was handed over (sometimes translated to betrayed), Jesus took bread....

The Greek word Paul uses is Paradidomi. This word literally means handed over. If Paul had wanted to say that Jesus was betrayed, he would have used the word Prodidomi.

Also suggesting that Paul didn't know of the betrayal is that in 1 Cor. 15:3-8, he mentions that Jesus, after the resurrection, appeared to the 12. While Paul could possibly be using the 12 as something more symbolic, coupled with other things he says, it seems unlikely that he knew of the story of a betrayal.

While Paul seems unaware of Judas, most scholars still think that Judas was a historical figure. John P. Meier, in his article, Criteria: How Do We Decide What Comes From Jesus? accepts that Judas is a historical figure. There really is no debate on the topic.

Part of the reason that he is excepted as a historical figure is that it's a tradition that doesn't seem plausible to have been made up by later Christians. As Bart Ehrman argues in a few of his works, but probably best in Jesus: Apocalyptic Prophet of the New Millennium, is that Jesus assumed that the 12 would rule with him. That was part of the Messianic understanding. So Jesus would have specifically picked Judas to rule with him, and for Judas then to betray Jesus shows fault with Jesus.

What we know for sure though is that Judas was part of the early tradition. He appears in all the Gospels, and by that time, he is cemented into the tradition, and we can be sure of that because he appears in both the synoptic Gospels (Mark Matthew and Luke) and John, so we know the tradition was large enough that both communities knew of it.

So we can be fairly certain Judas existed and betrayed Jesus. As for how he was betrayed, the story is a bit less clear. In John Dominic Crossan's book, the Historical Jesus, we do find a few issues with the traditional telling. First, it seems unlikely that Jesus knew Judas was going to betray him and outed him before it happened. The reason that is unlikely is because later on, when the betrayal takes place, the disciples are ready to fight those trying to arrest Jesus. If Jesus would have pointed at Judas, and said you're going to betray me, he probably wouldn't have had the chance to even leave. When Jesus is arrested, it appears though that his disciples are truly surprised.

Crossan and others have suggested that Judas probably betrayed Jesus more because he was trying to force the hand of Jesus. Ehrman really pushes this idea in his book by focusing on the apocalyptic nature of the teachings of Jesus. The idea was that the Kingdom of God would replace Rome, and the Messiah would bring that to being. Judas took this very seriously and wanted to force Jesus's hand to make this happen more quickly, believing that if he turned Jesus into the authorities, Jesus would have to act in a miraculous way. Instead, Jesus was crucified.

Interestingly enough, later Christian writers take on a similar look. In the Gospel of Judas, written in the late second century, the story is that Jesus asked Judas to betray him because it was necessary that Jesus be crucified. So Judas took the terrible job and set into motion the events that led to the crucifixion and resurrection.

Another interesting idea is highlighted in Hyam Maccoby's book, Judas Iscariot and the Myth of Jewish Evil. Most interesting is the argument that Judas was the brother of Jesus, and may have become the leader of the Jesus movement. Maccoby argues that Pauline Christians hid that fact and portrayed Judas instead as the betrayer. His argument really isn't accepted by other scholars, but the suggestion that Judas and Jesus were brothers is a view that has been repeated quite often.