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

However, they do have a significant goth influence and even have some goth songs in their repertoire, like "קפטן נמו".

If you want to dive into the goth music scene, some of the bands that might appeal to you if you enjoy Tattoo (טאטו) are HaPleez (הפליז) and Minimal Compact.