You can oak anything, but the question is if the oak flavors compliment the flavor of muscato.
IMHO, muscato has a distinctive fruity, light, and crisp flavor. The last thing I would want is more tannins and oak flavors would compete and not enhance the all over experience. In short, and in my opinion, oak has no place there.
To my tastes, the only white wine that benefits from oak is Chardonnay. This is simply my opinion and others may disagree.