Possible? Yes, though I'd recommend a shorter, high-heat cook with foil. Some cook it under something (like butt) that will drip on it and baste it; others put bacon on top, but I've never been a fan of this approach.
I'd seek a better source. Apparently Wal-Mart has whole Select packers. Ask arond elsewhere as well. Many places do not display whole briskets but have them in the back.