Yes, drilling in the ANWR would reduce our foreign oil dependence, and will help move the US to utilize our own energy sources. It will also lead to more effective competition on the world stage, as the majority of the world's oil is owned and sold by a few small countries. It may also help to boost the world economy, and level the playing field for oil companies moving forward.
Oil drilling in the Arctic National Wildlife Refuge will not reduce the United States oil dependency significantly. While drilling in the Arctic National Wildlife Refuge will help with the United States dependency, it will not impact it significantly. Drilling in the ANWR will only ruin the wildlife there, and the cost does not out weigh the benefit.