Well, Judas had already made plans to and agreed to betray Jesus (Matthew 26:14-16) before the last supper (Matthew 26:21), so in effect the betrayal had already begun at the time this painting is depicting. At the same time, Jesus spends a lot of words here repeating that the betrayal has been foretold and has to happen (Matthew 26:53-54), to in a sense Judas did have to betray him, as was foretold. Depends on how you think free will and prophesy interacts. (All references from the New International Version of the Bible at biblica.com)