No, Josef is not Becca's grandfather. He is a very important character, however, because he fills in the blanks in what Becca knows about her grandmother's life.
Josef is a homosexual who was targeted for the concentration camps by the Nazis because of his sexual orientation. He meets Gemma at the camp called Chelmno, where he witnesses people being gassed to death. Gemma was one of those victims, but Josef revived her with CPR. It is this act which causes Gemma to compare her experience to that of Sleeping Beauty; she calls the CPR the "kiss of life."
Gemma falls in love with and marries Josef's friend Aron Mandlestein.