Whether the pointedness of the object really makes any difference I don't know, but there is an argument to suggest that it might.
The negative charge in the cloud is going to induce a positive charge on the ground and anything sticking up from it like your copper rod. If you take any (conducting) object and charge it then the field gradient will be higher than the average at any pointy areas on the object. This is responsible for the corona discharge that you see when a pointed object is highly charged. This happens because the field gradient at the point is high enough to ionise air molecules.
So the argument is that the pointed object will have a higher field gradient near it and will therefore attract the lightening bolt. You certainly see this effect in the lab with a Van der Graaf generator. My only reservation is that I suspect the path of a lightening bolt is controlled by many factors and the pointedness of the lightening conductor will be only one of the factors.