Yes, with a little more care. Keep a removable, washable cover on the shikibuton and change it more often, remove pet hair from the surface regularly, and deal with any accidents immediately, because a shikibuton cannot be washed as a whole.
Pet hair
Wash the sheet or cover every few days if your pet sleeps on or near the bed. When you air the shikibuton, remove loose hair with a lint roller or a vacuum’s upholstery attachment on low suction.
Accidents
Blot immediately with a dry towel, spot-clean with a damp cloth and mild detergent, and dry the area completely before folding or sleeping on it. If a pet regularly shares the bed, a protector under the sheet adds useful protection; if it is waterproof, air the shikibuton more often.
Claws and daytime use
The cotton cover can be snagged by claws. Folding the shikibuton away each morning, which is the traditional Japanese routine anyway, also keeps it from becoming a daytime pet bed and limits the hair it collects.
HIMARI 日葵 and SORA 宙 have the same 100% cotton cover, so the care is the same for both.