Can the bank file a judgement (charge off) on an account for a minor?

You need legal counsel for this one. While you can open an account for a minor, whether or not you can file a legal action for collection of any overdraft against a minor it a whole other issue.

§ 6.2-896. Deposits of minors.
A bank may establish a deposit account for a minor as the sole and absolute owner of such account. The bank may receive deposits by or for such minor, honor any withdrawal request of the minor, and act in any other manner with respect to such account on the minor's order. Any payment or delivery of funds from such account to the minor, or the payment of a check or other written order for withdrawal of funds signed by such minor owner, shall be a valid and sufficient release and discharge of such bank for any payment or delivery so made. The parent or guardian of such minor shall not in his capacity as parent or guardian have the power to withdraw or transfer funds in any such account unless the minor has given written notice to the bank to accept the signature of such parent or guardian.