No. At least not without having everyone look at you. We would understand it, but it would be as if I said "Good New Year" instead of "Happy New Year." These phrases are so well known so you just say it in the one way.
They're just all different. There's not really a specific way to wish someone a good/happy holiday. Some have their own special phrase, like "Merry Christmas", but you can't really go wrong with "Happy [holiday]", though it might sound odd for some.