No, Nine Inch Nails is not a goth band, because they play Industrial, while goth music consists of Gothic Rock and its derived genres, like Deathrock, Darkwave, Ethereal Wave, and Coldwave.

If you want to dive into the goth music scene, some of the bands that might appeal to you if you enjoy Nine Inch Nails are Diva Destruction, London After Midnight, and Switchblade Symphony.