Hardly. There was an extensive number of heirs in the male line and plenty in the female line if the male line got taken out in their entirety, which is highly unlikely.
Assuming Alexander's often ill son Grand Duke George was with the family on this rare occasion instead of vacationing in warmer climates, Alexander would be succeeded by his brother Vladimir. He was as conservative as his elder brother, his wife Grand Duchss Vladimir was also a hardliner.