Short answer: not really. Well, they could but there are a number of ways to avoid it.
BBVA has announced they will charge €2 to those who want to operate with the teller, instead of going to the ATM, for operations under €2.000.
The first way to avoid the charge, if you have cash in your account, is to add €2.001 to the amount you want to withdraw and immediately afterwards deposit €2.001. Say you need €60. Withdraw €2.061 and deposit €2.001. You have your money and have complied with the requirements to avoid the charge.
The second way is to simply ask for spare change. You want the same €60 as before. Say that you have the imperative need to have €61.42 (or any other amount requiring coins). As per Central Bank of Spain rules, you have the right to have coins dispensed to you by the bank and, if the ATM does not give them to you, the teller must give them.
There is another implication to this abuse: if the bank is forcing you to use the ATM, they cannot charge you a commission for the debit card that you need to complete the operation. Operating with your account is already paid by the administration fee you pay, so you cannot be charged twice for the same service. If they insist on having their two Euros, even if they don´t because you don´t use that service, you can claim back the €36 or similar amount they are getting for the card.