Not really. I have overdraft protection disabled on my Ally account. I get fees all the time when it is overdrafted anyway. I really do want to punch the person in charge of letting accounts go negative. I would rather get denied at the POS than overdraft and suffer fees.
In Germany, we have special automated loans ("Dispokredit") for this situation. These are expensive (14% p.a.!), but as they are meant to be used only in emergencies and for a short time only, such a situation as here would not incur fees above 1€, as the interest is most often calculated daily.
Not all banks are this customer-hostile, luckily. But there may be undocumented ways to truly get this shut down. If not and if possible I’d recommend switching banks.
Open a Fidelity Cash Management account - they do exactly that, deny the charge with absolutely no fee. I accidentally chose to pay with my bank account instead of my credit card on PayPal, the charge was denied with no fees. On top of that the account has no account fees, no minimum balance, free checks, and ATM reimbursements.
I have 1 special account for these type of things, and I keep it empty or with just enough $ to cover what is rightfully owed.
I am no genius. I have learned my lessopn (from PayPal).