Does the castle construction order matter?
Apparently there are a few unlocks that require building up the castle in story mode, does it matter which order I construct the pieces?
In a very simple way, yes
According to IGN's Guide on story mode, each part of the castle you build unlocks specific levels, and certain parts of the castle can only be built once parts below them have been finished. After certain parts of the castle are built or interacted with, additional levels become available via new characters that appear around the castle construction area.