Yes. It is true. It also coined the German term for copycat suicides - "Werther-Effekt".
Goethe was addressed in person by a mother of a boy who loved his book and he did show remorse himself in a letter to Christine von Lassberg. In 1775 both the book and the Werther dress were banned in Leipzig since some boys would even dress themselves like Werther (a blue jacket + a yellow waistcoat) for the edginess.