Yes, that is a good size for an adult beardie, I wouldn't go any narrower than 18" though. He would have plenty of space.
My adults are in 42"long x 24"high x 21" wide vivs and have enough space.
Keep in mind they should be able to get to within 8" of a UVB (if your using a tube bulb like Retisun 10.0), so you may have to use command hooks to mount the tube lower in the tank, or raise the basking spot.