Your abs and erector spinae stabilize you as you do most, if not all, of the things you do daily. While you run, your abs keep your body from flailing around/wobbling. Say you're doing tricep pull downs with your back on the pad. Your abs/lower back keep your body straight. Try doing tricep pulldowns after a ridiculous amount of crunches and you'll feel what I'm talking about.
Just as the previous posters said, it will not substitute an abdominal workout by any means. As it is called, your "core" (abs and lower back) stabilize your body. It is vital to keep them strong.