Yes, a full freezer retains more cold when the door is opened. With a half-empty freezer, a lot of cold air will escape whenever the door is opened and more energy is than needed to bring the freezer back down to the right temperature.
Try to freeze small quantities of food at a time, separated out. Once frozen, pack them together closely. Remember to rotate food regularly and label it, or what you lose in wasted food will cancel out what you gain in energy savings.