I don't think it would necessarily follow. For Jesus, in making His statement, was not making a logical syllogism. He was expressing His emotion, His disappointment with Judas' betrayal — one of the special 12 whom He had chosen.For your understanding to be true it would necessarily follow that Judas would have been uniquely required for the crucifixion of our Savior to occur. No Judas, Jesus escapes the cross. I think God is more capable than that in carrying out His plans.
Here is another example of an emotion which in itself is not logical. A boy has been beaten by his father throughout his childhood. When the boy becomes 18, he angrily confronts his father. Among other things, he says, "I would have been a lot better off if you had never been born! I would have been a normal person." Logically this makes no sense. For if the boy's father had never been born, the boy would never have existed.
Often, emotional reactions trump logic.