Is it possible to get 99 rarity items from the Mystery Box?

thanks!

Yes. I don't know from personal experience but awhile back when Seedlings was the shop for the day, several people posted about getting the Ornate Floral Pitcher from the box.

loads of users (self included) have gotten r99 from MB esp when it parks at the apothecary c:

It's possible but it's even rarer than restocking from the shop. The Sable Smithy (today's shop) and work like that.