No, Fall Out Boy is not a goth band, because they play Pop Punk, 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 Fall Out Boy are Bauhaus, Siouxsie And The Banshees, and The Cure.