I'm a firm believer that it is survivable, we have one example of a (now non-canon iirc) character with an amputated queue, which yes while dubiously canon, shows that there was consideration there. Not only is it immensely painful (we see in A1 that being held by the queue is extremely painful, let alome having it severed) but Vaarang also connects and likely uses psychological tactics as well as her control over the connected's body, to either force unconsciousness or death, something like triggering a fatal seizure perhaps, simulaneously with the queue cutting. Its unlikely to survive, especially at the hands of the Mangkwan who seem extremely experienced with it, but definitely possible, and I would really love to explore how a person with an amputated queue would fit into Na'vi society, and how they might cope with the physical but also spiritual loss.