[JoshTriplett]

That depends heavily on your control system and how well you've tested it. In theory, a control system for a quadcopter that has independently controllable rotors could keep itself stable if one goes out. In practice, any control path you haven't tested probably won't work.

[JshWright]

The biggest issue I see is dealing with the unbalanced torque... You could probably manage a 'controlled crash', but that's about it.