Understanding and designing nanoscale interfaces are essential to advancing the thermomechanical performance of polymer nanocomposites reinforced by nanocellulose. In this context, it remains to be understood how disorder introduced on the surfaces of crystals as filler materials during extraction and processing influences interfacial adhesion with glassy polymers. Using atomistic molecular dynamics (MD) simulations, here we systematically explore the interfacial adhesion between nanocellulose and poly(methyl methacrylate) (PMMA) by comparing an ordered cellulose nanocrystal (CNC) interface to a disordered amorphous cellulose (AC) interface. Using a bilayer system that consists of a cellulose underlayer and a polymer upper layer, our simulations show that the AC PMMA interface can achieve about 50%-60% greater interfacial adhesion energy than that of the CNC PMMA interface. We uncover that the improved adhesion primarily arises from a larger number of hydrogen bonds formed between the cellulose and polymer chains. Remarkably, the greater adhesion energy and smaller filler filler surface energy achieved by the AC lead to significantly improved dispersive capability of nanofiller in polymer matrices in comparison with the CNC. Further analyses reveal that while the polymer chain configurations are characteristically different near the two interfaces, where stronger ordering and denser packing of chains are observed near the CNC, their relaxation dynamics are quite similar for the two interfaces. We attribute this observation to the competing effects between the interfacial adhesion and chain packing on polymer relaxation. Our study provides fundamental insights into the interfacial mechanisms of polymer nanocellulose interfaces at a molecular level and reveals that surface disorder inevitably introduced during production may serve to improve interfacial adhesion energy with the polymer matrix while also enhancing nanofiller dispersion within polymer nanocomposites.