If the account is originally yours, and they do get the account banned. (Worst case scenario)
You will always technically be the owner of the account, and therefore can always get blizzard to recover the account for you. Completely change everything on it like security questions and all.
Seeing as they don't have a id scan. You should be fine, you might be without an account for a bit, but you won't lose it for good.
Don't worry.