I received an email today from an organization asking me if I would rather not receive paper copies of its publications. The message title included "Save a Tree". I don't think that this organization or any other is so much interested in saving trees as they are in saving money. Putting out a glossy magazine ain't cheap.
Additionally, growing trees for pulp can be a sustainable enterprise. Cut the trees down and some more grow up. Let the trees stand too long and they rot and die. Of course, trees as a group were doing fine before the saw was invented.
What reducing the demand for paper might do is to reduce the opportunity and incentive for non-sustainable practices.
Still, I think most save-a-tree campaigns are either a feel-good endeavor or a cost-cutting move.
