It is possible to purchase sea dragons. You'll need money.
They are kept by individuals, "hobbyists," as well as public aquariums. They have been bred and the fry raised in captivity.
That all said, it isn't going to be a cake walk to get your hands on one, especially (from what I have heard) in the United States. And then, if you want to enjoy it, you've got to house it properly. That would mean, a big tank, a temperate tank, (not a reef tank), and, most likely, lots of live food.