Would it help to put a shade over the air conditioner unit?

In short, no. Home Energy magazine online from Sept 1995 used data from the Florida Energy Commission to show that in most cases adding shade using small trees or a trellis or something will not help. It may drop the temperature of incoming by up to 3 degrees, but because the A/C pushes such large volumes of air (250,000+ cubic feet for a 5ton A/C) cooling the small area directly around the A/C will probably not do much. If the A/C is located in shade of the house or of several large trees which will cool the air all around the unit, this can have an effect, especially if the trees also shade the house itself. In fact, if you impede the airflow by putting "shade" too close, you can decrease the efficiency of the A/C. One thing you can do that may improve efficiency is to cool the house more during the cooler hours of the morning (especially if you'll be there during the day) and maintain the cool temperature during the day. Remember that heat is absorbed by more than just the air in the house itself - the walls and floor adapt to the temperature of the warm air and release the heat when the A/C cools the air inside.