If someone converts to Judaism, they are concidered to have become part of the Jewish people as well as the Jewish religion. Thus, while a geneticist will disagree, the convert is a descendant of Avraham by Sarah through the line of Yitzchak and Yakov. My father is actually a convert (as an adult, by his own choice, not my mother's) from Catholicism. As far as Jews are concerned, be they Reform, Conservative, Orthodox, Reconstructionist, Hassidic, or whatever he is concidered fully Jewish in blood. In fact, it is concidered a horrible taboo to ever remind someone that they are a convert. Furthermore, King David's own grandmother was a convert!
That definition was created by the Nazis and has no basis in whom Jews consider to be Jewish or whom anyone else with any education in the matter considers Jewish. The grandparents rule is ridiculous and should never be concidered to have any bearing.
EDIT:
Messianic Jews are not Jews, they are Christians pretending to be Jews.