YES, it is grammatically correct. ALL is an adverb which means "completely" therefore-- i am all happy = i am completely happy.

Hi Iris, I would not use that phrase as it does not sound quite right. They're "all happy" We're "all happy" To keep them "all happy" everybody is "all happy" etc; Possibly a person could say I'm feeling "all happy". Hope that helps :)

I think this technically could be correct grammatically, but it sounds unnatural. I would say "I'm completely happy." or "I am very happy." instead. Those both sound a bit more natural.