No, Faetooth is not a goth band, because they play Sludge/Doom Metal, Shoegaze, 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 Faetooth are Lycia and Trance To The Sun.