Is this a true translation of a famous quote?
Almost.

Translating「瓦全」as a whole piece of clay, in my opinion, is not immediately intuitive (and that's not really what the literal translation is anyway). I would translate「寧爲玉碎不爲瓦全」to


  Better to be shattered jade than to be flawless china.


The message is: A principled person would rather die upholding righteousness than to live an ignoble existence.