Sorry for the late reply.

That's an interesting question - would a unit test prevent this error? To answer this, let's consider what happened: the database didn't respond in an appropriate way, and probably returned an error. I'm not exactly sure what exact error was displayed, but WordPress has caught this situation, and handled it the best it could - displaying a proper error. I would write a unit test for this exact scenario - using a fake (mock) object, simulate the database timeout, and make sure that the error was caught and handled appropriately. Other then that there's no real other way to gracefully recover.