In the history of the award, only 3 players have hit .275 or lower and won the award. One was Roger Marris in 1961, one was Zoilo Versalles in 1965 who hit .273/.319/.462 but lead his league on total bases and the other was Yogi Berra in 1955.
So unless Granderson sets a new MLB record for home runs, leads his league in total bases or is a catcher, he's not winning.