Do Mark Anthony and Cleopatra have living descendants?

Absolutely yes. Genealogy information of their family lines had been drawn together by professional Egyptologists and historians, leading to the conclusion of many, thousands even, descending from Marc Antony and Cleopatra VII.

For more information, you may want to look into on-line ancestry and genealogy websites. Most of them now have Cleopatra's pedigree on-line available to view.