Fractured Humerus

My wife took a bad fall on her shoulder and fractured her humerus about 2 inches below the shoulder ball joint. The emergency room doctor said it was displaced about 40% and said surgery was NOT indicated.  She was given a sling and sent to an Orthopedist who said the same thing - surgery was not indicated, but that it would heal on its own.

I've seen the x-ray, and frankly am disturbed by how the bone looks all out of place, yet I like the doctors who say that they don't think setting it and pinning it is a good option.

My question is this:   can the bone heal being 40% displaced?  Will my wife regain 100% use of her arm even though the humerus is displaced?  I just don't see how it can heal.

Thanks,
Carl