No, The Smiths is not a goth band, because they play Jangle Pop, 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 The Smiths are Autumn's Grey Solace, The Cure, and The Mission.