i was experimenting with iOS 9 Notes.app and I tried enabling Google (Gmail) IMAP sync. It worked for one of my Google accounts, but not for another.
The trick was Gmail Settings:Labels. I had to check the Notes Label Show in IMAP.
After doing this it worked again. I’m sure if you have IMAP disabled in Gmail it will similarly fail.
This old school IMAP sync tech doesn’t support the new rich-text-like Notes documents, only plain text notes. It’s really a legacy feature that will likely get dropped in iOS 10.