I'm sure someone's done it on a thumper. Back in the day you didn't go buy a special purpose bike, you used what you had and made due with it.
I am definitely in agreement about the tires and the fuel capacity. There are places you'll need to do well over 200 miles to get to the next fuel stop. Just think about those frost heaves with and inch and a half of suspension travel. There's hundreds of miles of gravel, hard packed to loose and squishy. Turns into a slick muddy mess when it rains.
That would be an awesome ride. I'd love to see all that scenery first-hand. I've been wanting to do that for the last couple of years. But, I can't take the time off from work and I certainly don't have the funds for a trip like that.
Here's a link to a girl that did the trip from Virginia to Alaska and back on an old Yamaha Radian.
http://advrider.com/index.php?threads/virginia-to-alaska-and-back-on-an-86-ya...This one's a guy who did it on a dual sport. He's got lots of information about stops, costs and stuff in his write-up.
http://advrider.com/index.php?threads/alaska-adventure-broken-bones-kamikaze-...Both of those links will probably put you near the end of the write-up, just go back to 1 and start reading.
I wish I could do it but I doubt I will ever make it. Maybe if I win the lottery or something.