It depends on the pillow quality and the cover. Some pillows have special technology that can withstand outdoor elements. On the other hand, the cover should also have high-quality fabric material that can protect everything under it from environmental elements, such as the sun’s heat, rain, mold, and mildew.
Otherwise, it is not recommended to put the pillows along with the furniture under the cover. However, if you still decide to do this, make sure to check your pillows from time to time and let your pillows “breathe” along with your furniture especially during good weather days.