Does the child need to be educational diagnose to have ABA therapy?
Yes this is true in most states, if you want the school to pay for the ABA then you need the school evaluation for them to do that. You will have a fight on your hands with insurance as well if it is the law in your state that the school district pay for it. I know it is time consuming and frustrating but the evaluation will benefit you in the end so I would have one done.
If you want to get it from your school system (if they offer it) then yes, your child would have to be evaluated by the school system to determine their educational needs.
If you are looking to do it privately through your insurance then they need a medical diagnosis for for, and possibly an educational evaluation because sometimes insurance doesn't want to pay for something they think you should be getting from the school.
If you are in a position to pay out of pocket for private therapy then no, you can hire a therapist to do whatever you feel your child needs regardless of diagnosis.