I guess a lot depends on what your professor meant by “literate.” Faulkner is, by most reckonings of the last forty or fifty years, in the top three of the most important and influential American novelists-—the other two being Hemingway and Fitzgerald, with Fitzgerald as the weakest link IMHO. So if literacy is dependent on familiarity with the history, influences, and traditions of American writers, then Faulkner is a must read with at least a few novels and handful of short stories.
Whither or not you’re missing something by not fitting this definition of literacy is an entirely different question. There will be some people out there who would make some sort of claim about white men missing out by not reading the works of Terry McMillan, but I’m not about to buy any of her works from Amazon.com anytime soon.
But don’t let a professor’s opinion prevent you from reading Faulkner. I happen to think he wrote some great books. The Sound and the Fury, * Sanctuary*, As I Lay Dying, Light in August, Absalom, Absalom!, The Hamlet, et al all come to mind as truly excellent novels whither you want to be literate in American literature or not. Read him because he wrote great books, not because a professor will think less of you if you didn’t.