Yes. Everything that they are trained and able to do here, is covered by the national insurance, at least where I live.
We never even have to explicitly ask them to approve anything, it's all automatic. You don't see the bill.
You might have to pay the difference for "nonessential upgrades", like a plastic cast instead of a normal one when you break your arm. Had to pay 5.00 EUR for that and it was the only time I had to pay out of pocket in my entire life.