The only stupid question is one that's never asked.
There is no definitive answer to your question as asked because it depends upon the size of the puffer and the type of sea urchin, but basically, yes.
The puffers most likely to kill urchins in the home aquarium are the smallest, ie the tobies who would happily munch away at tube feet all day long.
With your more common puffers (Arathon sp.) will generally ignore all urchins unless the specimen is in the HUGE category, meaning a foot or larger.......at this size, if they decide the urchin is edible, it's lunch, shell, spines and all, but this is still unusual.
The family of fish most noted for destroying urchins is the Triggerfish, who are closely related to the Puffers, with the predator/prey relationship between the Queen Trigger and the Atlantic long-spined urchin one of the most famous, to the point that a very stupid Florida law was passed by a well meaning, but not too swift politician.
Urchins, by the way, are also accepted as food by and preyed upon by Harlequin shrimp of starfish eating fame.
Mike