Parts of Alaska are as remote as any place on earth. You'd really need to know your stuff.
A USGS study of the lower 48 states about 15 years ago found that there was no place--no place--that was farther than 25 miles (as the crow flies) from a road of some sort (including Forest Service roads).
That is not the case in Alaska. Quite a few folks that go trekking just vanish up there: starved, drowned, frozen, killed and eaten, fall into a crevasse. It's where you can be certain that the universe is not friendly. There are even spots in Alaska where you can't even tweet.
I would probably have jumped at the opportunity in my late 30s--a time in my life when I still wanted to see everywhere in the world. Since then, I've been to enough places that I wish I hadn't been, that I pick and choose my destinations with more circumspection these days.
My take on how much food you can realistically carry is 10 days worth in a reasonable pack. If you happen to be a brilliant planner, you might be able to eek by on 1 pound of food a day, for 10 days, but that requires some pretty poor choices for long-term nutrition. If your cooking fuel is collected dead wood (no longer permitted in many Federal and State managed areas), then the 30 days might be within reach. Otherwise, cooking fuel alone is ~4-5 pounds. With uncertain water sources, you would need to carry 6 liters of water (~12 pounds), which is really only about 2 days worth. And we haven't even started with gear.
That's not to suggest that a 30 day trek can't be done. NOLS (National Outdoor Leadership School), in Wyoming, routinely does them across the globe.
http://www.nols.edu/courses/find/byskill/backpacking.shtml
But they have some of the best wilderness instructors in the world. (You're less likely to die.)
Bob