How to search for a character in the special characters window?
Ctrl+Option+Space in 10.9.x brings up a quick access to special characters in line where you're typing —throughout most every app.

The search algorithm is the same of course, which it seems relies on how the charicter is tagged rather than a smart search throughout.

Still, in general, I have found the quick access shortcut and search to work well for most things. If you start typing while the special char fly out is open it will run a search.

Interestingly, While it seems that some older special characters like π have names that need to be entered exactly to search for them  "small greek letter pi = π", emoji will display if just part of the name is searched. "Person with blond hair=" can be searched just by typing in blond.