There are so many conflicting reports of online or not now, I don't know what to think.
At E3, Reggie said GH III would have online play. Also, the other day IGN said that GH III had online play but they couldn't play it on the demo.
Now, there is this interview posted today and a similar article was on Kotaku the other day.
What to believe? I seriously doubt that if GHIII doesn't have online on the disk, it will never have it. No game has ever taken advantage of Wiiconnect24 features. I don't see that changing.