The world absolutely can survive without the Dollar as the reserve currency. China and many other countries would eventually be fine without it. The US would eventually recover, too (although probably not to where we are today). The problem is that the transition would be very very painful.
The world will survive ultimately (no doubt about it), but the standard of living will fall down dramatically, at least temporarily. And the more developed a country is, the more it is intertwined into the global economy, the stronger will the impact be on it.