No, not necessarily. While you shouldn’t scuff your feet along the carpet and then try to zap the boards, they’re pretty robust with respect to general handling.
For long term storage, preventing moisture should generally be the chief concern– store vented in a cool dry place, or sealed with a desiccant.
Antistatic bags will work fine, as will polyethylene bags (those made of the same type as ziploc bags). Avoid other types of plastic, especially styrene, acrylic, and other types that seem particularly “staticy.”