No, Modern English is not a goth band, because they play Post-Punk/New Wave/Jangle Pop, while goth music consists of Gothic Rock and its derived genres, like Deathrock, Darkwave, Ethereal Wave, and Coldwave.

However, they were an important influence on the development of goth music and are respected in the goth scene.

If you want to dive into the goth music scene, some of the bands that might appeal to you if you enjoy Modern English are Bauhaus, Siouxsie And The Banshees, and The Cure.