(To get technical, the blood get stuck in there, loses its oxygen, and you end up with the same problems you'd have with any other body part that had its circulation cut off.)
It turns blue and falls off?
I suppose theoretically it could, if the priapism lasted for a solid week or so. But the doctors in the ER usually treat it by shoving a needle in it and draining the blood. :)
What the general danger is, though, is that the blood vessels in it (of which there aren't that many) get damaged, and you end up impotent.