I have no idea on the rental bikes but I have ridden to Alaska twice.
Paved roads all the way if you choose. If you have 3 to 4 weeks why miss the great American West? Watch the enclosed video and see what you will be missing.
If you feel you can't ride dirt go to BMW's Enduro training course in South Carolina and then follow it up with Jimmy Lewis's course down in Nevada. Or just go to Jimmy's course and you will be looking for dirt.
You could ride up from lets say Seattle and then float with the bike back down.