Depends on your definition of "failure".

If the battery has run flat because the car has been parked up for many weeks doing nothing then the answer would be no. Most car batteries will run out of charge if the car isn't used for long periods. And jump-starting the car incorrectly can cause terminal battery damage that will prevent it from holding a full charge ever again.

If, on the other hand, the battery has suddenly stopped holding a charge and car usage isn't to blame then I would say yes, the dealer is liable. A battery shouldn't suddenly fail. If it does, I would argue it had a preexisting fault at the time you bought the car.