Yes, they can. For best results, wash them rolled up on a delicate setting at no more than 40C. Remove from washing machine immediately. Tumble dry on a cold setting rolled up or line dry in summer and over the banister in winter. Incredibly, the soft cotton voile fabric gets softer with each wash.
Please note that quilts using vegetable dyes fade naturally over time due to the absence of chemicals to set the dyes. Wash dark colours separately. Some people prefer to dry clean them to minimize fading.