Personally, I wouldn't trust a cat being along with a beard dragon, but it is possible nothing will happen. It really depends on the personality of the cat. You know many cats are too "playful" with other animals. Sometimes they like to bully or even kill other smaller animals just for fun. Cats are in fact the #1 killer species in the world since they kill more than 1,000 other species. All the other predators only kill the same a few dozens species at most. I saw that one on Animal Planet where it was about "Top 10 killers" or something similar to that title.
If you absolutely want to have both a beard dragon and a cat, you might want to try it this way. Keep the beard dragon in a "cat-proof" enclosure. Allow the cat into the same room and watch the cat's reaction. If the cat shows any kind of aggression or too "playful" toward the beard dragon, I don't believe this cat is safe for beard dragon lol. Although, you can still have the beard dragon as long as you keep it inside the closure or play with it without the cat being in the same room.
