Can publication work against an applicant to an MFA in Creative Writing program -- is it possible to be considered too experienced? I was rejected last year with a portfolio that included several published pieces (novel excerpt, short fiction and non-fiction.) I don't think I came off as arrogant in my cover letter, but I probably sounded more confident than I am -- I have a lot to learn and badly want to learn it.
AA, it might work against you, so I'd be sure to address it in your personal statement. Do so directly, clearly, and briefly. Focus on what you'd like to get out of the MFA experience. I like that last sentence of yours: "I have a lot to learn and badly want to learn it." That's the right tone. Don't worry it too much: many have been published before. Unless you come across as arrogant or beyond learning, then I'd be surprised if it cost you a spot. Good luck.