I can confirm that Chocobo Barding works.
My Chocobo did wear for a long time the Gridanian Hat (Feather), the Uldahn Body and the Lominsan Legs armor.

This however only works if you equip the piece while you belong to the corresponding GC.
Once you change, you get to keep it on your Chocobo, but once you remove it, you cannot equip it again.