Alaska being Geographically separated from the rest of the US would stand a better chance than any other state. We currently have dealings with Canada, with whom we share a huge border. We deal with Korea, Japan, China, Russia, and all around the Pacific rim. We sell them raw materials, and we get manufactured goods, and produce, in return.
We could live without the rest of the US. While they might blockade our ports, they would have a hard time isolating us from Canada.