No, Swans is not a goth band, because they play Alternative/Noise/Experimental Rock, 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 Swans are Bauhaus, Lestat, and Lycia.