Could you post a close up please?

It probably will survive on it's own, most of the time drafting is done for slow growing plants. It is also used to propagate new 'creations' or discoveries to get many new plants to market fast. The rootstock is a vigorous growing plant. Hylocereus undatus and H. trigonus, Trichocereus spachianus and Cereus peruvianus are most often used as rootstock.

Plants that do not survive on their own are plants without chlorophyll & can't photosynthesize, so they are grafted. These are sold as 'Moon cacti'.

I have found mammillaria bocasana cv. Fred to be the closest match.

http://www.cactus-art.biz/schede/MAMMILLARIA/Mammillaria_bocasana/Mammillaria_bocasana_fred/Mammillaria_bocasana_fred.htm