Yes. The rate at which ice melts is directly proportional to its surface area. Now here's where that gets a little complicated... With a smaller surface area, the ice will melt faster, although if it is connected, it will by definition have a smaller surface area, however the individual parts will all melt at the same rate, therefore you treat each part as a separate entity.
Furthermore, the melting rate is also directly proportional to the smallest radius. If you have ice that's in a big ball, and you have ice in a stick that's as long as the diameter of the ball, but is only half as thick, the stick will melt twice as fast, because the smallest radius will be half that of the ice ball.
The fastest melting shape of ice would be one shaped like a koosh ball (http://www.edb.utexas.edu/ATLab/Clipart/devicepics/koosh.jpg). Note how it's comprised of lots of little thin sticks. Each of those would melt fast because of the small radius. The slowest shape would be a ball because of the even radius, so with a ball it depends solely on the size of it.