NO ,they are almost on the Endangered list.
Due to being protected by law, obtaining sea dragons is often an expensive and difficult process as they must be from captive bred stock, and exporters must prove their broodstock were caught before collecting restrictions went into effect, or that they had a license to collect dragons. To date, no successful, closed cycle, captive-breeding programme has occurred (i.e. getting a generation of captive-raised sea dragons to breed). Sea dragons have a specific level of protection under federal fisheries legislation as well as in most Australian states where they occur.
They are very fragile and unstable outside their natural habitat. Success in keeping them has been largely in the public aquarium sector, due to funding and knowledge that would not be available to the average aquarium enthusiast.