To quote the Smithsonian magazine: "divers found a pewter urethral syringe containing traces of mercury, which in the pirates’ day was used to treat syphilis" this would make people to speculate that at minimum someone on his ship had syphilis. Blackbeard had this syringe because he captured vessels at Charleston and his ransom was a medicine chest. It is hard to answer this because not much is known about his personal life.

Sources: "Queen Anne's Revenge." Ships of the World, Houghton Mifflin. Boston: Houghton Mifflin, 1997. Credo Reference. Web. 10 November 2014.
http://www.smithsonianmag.com/history/last-days-blackbeard-180949440/?all