No, Genghis Khan did not sack Rome. Genghis Khan, the founder of the Mongol Empire, lived from 1162 to 1227, and during his lifetime, his conquests primarily focused on parts of Asia and Eastern Europe.
The Mongol Empire expanded rapidly, but it did not reach the Italian peninsula until well after Genghis Khan’s death. His successors continued to expand the Mongol territories, but Rome was not a target during the time of Genghis Khan. In fact, by the time the Mongols reached Eastern Europe, Rome had already undergone significant changes and was not the powerful entity it once was.
Thus, while Genghis Khan and the Mongol Empire are known for their military prowess and conquests, they had no direct involvement with Rome in terms of sacking or attacking it.