I recently travelled from Kennedy to Sydney with a Martin 000 guitar in a hard case.
I didn't mention it to the check in people (but didn't hid it either.) It tended to fit in most overhead lockers and the airplane personnel didn't give me any trouble. On the last leg from Tokyo to Sydney the airplane had smaller overhead lockers. I refused to check it. It turned out that the first (or business) class compartment has a place to hang up coats. The stewardess put my guitar in there. That worked out quite well.
The 000 is bigger than the baby Taylor or the Larrivee Parlor, but then again, international planes are probably bigger than domestic ones.
Anyway if there are problems with the plane being crowded or the lockers being small, ask if it can be put in the first-class luggage compartment.
A friend of mine here, who sings professionally has even had the guitar ride in a first class overhead locker while he sat in a tourist-class seat.