Yep.
http://i.imgur.com/Is0bXxP.png
I have yet to see anyone post any logs showing that they fed the same food in a session and it skipped the feather message. I think it's RNG to get the chocobo to eat enough to actually be affected by feeding.
I saw one person post a log that had berries or something stop giving them the proc, and I suspect they found a color cap.
Edit:
@Amelia
Is what you've posted listing only the ones that got feather procs?
