There are so many aspects on this. I've been on a different journey: not enough Asperger to get a proper diagnosis and I have a little attention deficiency as well. My son (Asp diagnosis) is barely at school. So I have read up on this.
First: she may fit into an ADHD diagnosis, and it may or may not help her. She may lack a significant trait for the definition, and then she is sentenced "normal" and will thus not get any aid.
Trying to get a diagnosis may be futile. So why not take it more practical: this kid is overly active, there are with or w/o a diagnosis a number of things to do to circumvent what "trigs" an active mind, to calm her, make her focus and make her school days worth while.
Remember that school is a conformistic place where people (=kids) are supposed to behave in a conformistic manner. A manner that we adults prefer :)
Your granddaughter is hyperactive. Ok P.C. people get offended, let's call her highly active. It may give the following results:
She will overreact on external stimuli: "if the class runs, she runs. When the class stops she continues running, and may run into a table." "If on a hike she will follow all cars with her eyes, the class talks then she talks as well, when reaching the destination she is all worn out and teachers are irritated".
She may feel outside and different (due to her internal chaos or "odd behaviour") from the conformistic group. It may even end in depression.
Her behaviour may be tolerated by most kids, but there are the quiet ones (Asperger, ADD, HSP), dreaming/absent minded kids who eventually get their day ruined since she may (not single handedly, mind you!) rise the class' noise / disruption etc level.
That she didn't draw like the teacher said may not be "spite", maybe she just wasn't paying proper attention and then drifted away or even had a better idea!
School with its abundance of stimuli makes her tired and quiet: home is calm, there she can recouperate.
I suggest you read up on ADHD and the simple circumvention methods that are used, like a cubicle to sit in and work. One can even have "dyslexia in the ears": problem with remembering oral instructions, while written instructions are just fine: a simple piece of paper saves the day!
In my country some kids are seriously given ear protection at school in order to keep the world out!
ADHD people really aren't my cup of tea but that hyperactivity and that broadened mind that goes with it is really a good asset, if properly managed.
I seriously wonder if this is an epidemic in the western world.