No, Unheilig is not a goth band, because they play Neue Deutsche Härte, 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 Unheilig are Fields Of The Nephilim, London After Midnight, and The Last Dance.