In this work, we studied for the first time the formation of olive oil emulsions in water stabilized by plate-like nanocrystals with the supramolecular structure of cellulose II (pCNC). Effects of storage, pCNC concentration, and NaCl on the stability and properties of Pickering emulsions, including the creaming index, droplet size, zeta potential, acid-base surface properties, and rheology, were studied. A significant influence of the shape of nanoparticles (compared to the classical rod-like shape) on the stability parameters and rheological characteristics of emulsions is shown. Plate-like cellulose nanocrystals at a concentration of 16 g/L are able to form delamination-resistant emulsions without added electrolytes. The viscosity of pCNC-stabilized emulsions tends to decrease with increasing electrolyte concentration in the system, which is not characteristic of rod-like CNC-stabilized emulsions. This effect in pCNC-stabilized emulsions assumedly can be associated both with weak mechanical engagement between drops due to the shape of stabilizer particles and with an insignificant participation of background electrolyte cations in the formation of interdroplet interactions. Therefore, the resulting aggregates are unstable and easily destroyed, even under weak mechanical stress. As a consequence, the acid-base properties of the pCNC surface are practically independent of the emulsion preparation method (with or without electrolyte) as well as the concentration of the background electrolyte. The reduced viscosity of pCNC-stabilized emulsions in the presence of an electrolyte, coupled with the absence of acute toxicity, allows us to recommend them as a convenient oral delivery system for fat-soluble, biologically active substances. Our emulsions carrying donepezil (an anti-Alzheimer drug) showed better performance than a solution of donepezil hydrochloride in preventing memory impairment tested on laboratory mice.