Absolutely, anyone interested in drilling for oil in Alaska's wilderness should be free to do so. You used another tendentious word, "rape" as you spoke of "raping the earth's resources". If there is a concrete harm done by resource extraction, then that harm becomes the reason that makes such extraction unrightful. The absence of a government permit never becomes such reason under the natural law.
If that is true than Alaska ceases to exist. The territory that they claim, is no longer under the direction of the state soverigns. What if Alaska doesn't want people to drill for oil in their State?