No, Jesus is not telling Judas to go sin.
The trespass of Judas against Jesus was not the act of delivering him, but the making of the covenant to deliver him, after the devil put it into his heart. (John 13:2) That is the trespass depicted by the words of the psalmist: “[he] has lifted up his heel against me.” (John 13:18)
Jesus responded to that trespass by telling Judas he was not clean, and by washing him clean. (Matthew 18:15; John 13:10,11; John 13:4-12)
The act of delivering Jesus was neither a trespass against Jesus, nor a sin.
Primarily, God delivered Jesus. (Romans 8:32)
Secondarily, Jesus delivered himself. (Galatians 2:20)
Judas delivered Jesus as his servant, tertiarily--and only after Jesus raised him up again by washing him clean. (John 12:26; John 6:39)
Satan was opposed to the things of God that Jesus said must happen, and Satan, after the sop, acted upon Judas to make him opposed to delivering Jesus. (Matthew 16:21-23; John 13:27)
By his words, “That you do, do quickly,” Jesus prompted Judas to decide whether or not he would follow Satan or deny himself, take up his cross, and follow him. (Matthew 16:24)
Judas realized that the diabolical covenant he made to deliver Jesus had become his cross.
Judas, the first of the twelve to do so, overcame Satan and accepted the work for which Jesus chose him. (John 13:30)
That is why Jesus declared, “Now is the Son of man glorified. (John 13:31)
By doing the work given by another, one glorifies the other. (John 17:4)
And if the work is a thing of God, it is not a sin.