To maintain a pixie cut, some hair product will need to be used, but that could include items like mousse, hairspray, gels or pomades. Hairspray is not necessarily needed to maintain the look of a pixie cut, especially if one of the other products is used instead.
Different hair products result in different looks with a pixie cut; for instance, using a pomade makes the hair clump together more, giving it a textured appearance. In contrast, hairspray holds the hair in position, but it's intended to move more freely than a pomade. Gel may make the hair hard or crispy to the touch, and mousse adds volume to the hair.