I would call into question the definition of suffering. Does the "school" consider if there degrees of it? How is it quantified? How is it balanced? How objectivity factors into the equation, and what a lack of suffering would look like, mathematically?

Whether it's morally sound to conclude that any existence of some degree of suffering negates all value of all life, universally in particular, resulting in the duty of life to annihilate itself, I would give a resounding no. We are a mere dust, a fraction of the contents of the universe, and our annihilation may serve no more purpose than our preservation. In light of the choice, as you present it, we should choose life. We are not the drivers of life, nor of existence itself. This "doctrine" is vain and ignorant in that sense, putting more value on humans in the universe than what we deserve.

The only duty we may garnish from our existence is to abide by natural laws that we do not create. We do not have the capacity to destroy all life, because life is greater than us. It's not our place to decide whether suffering makes it "worth it" in a vast, violent, expanding universe that we cannot truly comprehend.

So, no, our 100% suffering would not mean that we should annihilate everything, to cure the universe. Life and suffering are not, unfortunately, mutually exclusive.