Does anyone know if the character add on pack includes character tuck boxes like the ones included in the base set?
Not sure what you mean. Where did you see that the base game came with tuck boxes? I know it comes with a box for the Burt Offerings adventure path, but I don't believe there are any other tuck boxes in the base set.
However, the character add-on pack DOES come in a tuck box, but it's just the general packaging...