What kind of border are you planning to add? I don't think I've ever seen a border added to a string quilt before. How wide will it be? Will it be pieced (like blocks of some sort)? Or solid, strips of fabric? If it is just solid strips and fairly narrow (like only a couple inches) you probably won't need a foundation.... But wider you might want one... Lots of variables, depending on the type/size of border.