Yes, it is a depressant. Narcotics are a different class.
Yes, I mispoke when I said alcohol was a narcotic. I should have said, "It's a depressant, with some narcotic effects." Because alcohol was in fact used as a narcotic, during the Civil War. (And there is truth to the Westerns that show people drinking alcohol prior to removal of a bullet.)
Here is a website with a nice animated-graphics presentation of the differences between classes of drugs:
Can you imagine the day after having that done? Besides the pain from the wound, there would be an awful hangover.