In a nutshell that is correct for most carnivorous animals. Cellulose is one constituent of the plant cell wall and is a polysaccharide. Carnivores in general digest saccharides quite inefficiently (compared to omnivores/herbivores)....very basically, carnivores lack the proper dentition, gut flora and enzymes necessary to digest cellulose. Cellulose (fiber) and other non-digestible materials such as chitin and bones that are not destroyed by stomach acid are passed into the feces.
I would agree that most caudates can digest animal material as they are carnivores. However, in that their natural diet is composed of invertebrates, other than for specific dietary reasons and to avoid the risks that have been outlined, I would wonder why we would not advocate minimizing their (pinky) use as a food source for caudates? In the wild, would axolotls have many chances to eat pinkies?