Cellulose is cellulose regardless of the source. Just because one paper may be made out of cotton lint (they really don't use rag stock any longer) or another is made out of properly processed alpha-cellulose really doesn't affect the property of the paper one iota. All that it means is that sourced cellulose is different.
Alan, I think from a chemical perspective you are essentially correct, and hence a high quality alphacellulose paper may very well have the chemical stability (and longevity) of a "100%" cotton paper. However, there are distinct material property differences between cotton and alphacellulose papers that do give credence to what Jim D is saying about de-curling as well as other materials handling attributes. The molecular chain lengths of the fibers can differ.
All papers have anisotropic material properties which leads to craft terms like "warp and weft" or "long-grain" and "short grain" paper characteristics. These material properties are influenced by the molecular chain length of the chosen linters, i.e., cotton or wood pulp, and many other factors as well, including the mechanical press properties of the paper making machinery. In other words, you could supply the same linters to two different paper mills and the products produced will still have different chemical, physical, and mechanical properties. Much of this reality is due to the fact that terms like "100% cotton" paper are really a misnomer. While the source of the linters used in the paper may be 100% cotton, the final product has many other chemical components including sizings, surfactants, whiteners, inorganic fillers like calcium carbonate, etc. Bottom line: cotton and high-quality alpha cellulose acid and lignin-free papers are still two very different final products. It's not just chemistry of the linters. It's all the other junk, plus the unique mechanical paper-forming properties associated with individual mills that produce the papers.