They can eat small vertebrates fine, as they do in nature. Although I would never feed any vertebrate mainly for potential parasite prevention and animal welfare reasons, especially if it is alive. In youtube you can find nearly anything, I saw once a video where a bearded dragon ate a small garter snnake. In other instance his owner gave it a centipede and a wild rat. Many such people seem to value the shock factor above their animal's health and well being.
Bearded dragons retain venom glands from their ancestors, but there has been no documented evidence that they kill with poison. They are mainly crushers and chewers like tuataras. The truth is that in most videos they are fed scorpions, the tip of the stinger was cut off. Sometimes they are given spiders but it isn't always dangerous. A gui in Australia gave his own a funnel web, which strangely happens to have serious even deadly toxicity for humans and other primates, but much less or non for other mammals and reptiles.