My question is, can this tree be trained like a conventional bonsai? Yes.
Will its lateral buds respond if/when I nip off a leading bud? Yes, but the enthusiasm with which the tree responds to the pruning will depend in very large part on when you do the pruning, how hard you prune, how much food/energy the tree has stored, and how much food/energy it's capable of producing (via photosynthesis) at the time the plant is pruned. Also, pinching out a branch's apical meristem does not guarantee that all latent buds proximal to the pruning cut will be activated. Trees vary in how they respond to pruning, but the only GUARANTEE is that the bud most distal after the pruning/pinching cut will be activated, but usually you can expect 3 or more suppressed buds to be stimulated to grow so they produce new branches.
Is there a trick in pruning its root system? No. Most young deciduous (younger than 25-30 yrs old) trees are repotted annually or every other year, depending on how aggressive the root system is. Repotting annually will conspicuously hasten the tree's development. Trees repotted annually or every other year typically grow at 5-10x the rate of trees which are only bumped up a pot size now and then or neglected altogether. If you'd like to see an example of what repotting looks like, just ask and I'll provide images.
I'd like to give it a shot, but don't see many hits when doing a search on cottonwood and bonsai. They're not often used as bonsai material because of their coarse growth (large leaves and long internodes), and their tendency to randomly shed entire branches you would consider to be an essential part of the composition.
Al