the answer is yes but since the rope passes through the atmosphere, you have to pull the rope with enough force to overcome the friction of miles of air against the rope's surface plus enough force to overcome the inertia any orbiting object would have that keeps it from falling in the first place, just to get it started on any new trajectory at all

but if you did the moon's new trajectory would make it fall to earth eventually, except that as it followed that trajectory the rope would wrap around the earth and pull it down harder, or snap