The candy eating badges culminate in Candy Stripper, for eating 353 pieces of candy.
You can only eat 11 pieces of candy a day before the Toothache debuff kicks in.
Therefore, each real-life 24-hour day, you can only eat 66 pieces.
If the Zille-o-ween event lasts less than 5 days 12 hours, this is impossible.
(edited since TomC says the debuff kicks in at 11, not 10)