If you did the survey for several people, the answer would tend to be yes. But one usually doesn't think about how this yes would be generated.
The first factor for preventing the destruction of Nature would be the principle that anthropocentrism was not important, but Naturalism. Anthropocentrism determines that the center is man, but if the center is man, then the basis of reality would be man's mentality.
But Nature does not obey man's mentality, nature follows physical rules and laws. Thus, to conserve Nature, human pleasures should be limited to preventive physical rules.
And that's the big human problem, following preventive rules. Usually man makes the mistake, suffers and then learns. That's if after time passes you don't make the same mistake.
But then is it impossible for man to have failed to destroy nature? It is possible, but man would have to change his culture from being at the center of everything. Every man wants his will to be the center of everything, living this lie.
The big problem of destruction is the so-called global footprint, global footprint is how much man marks nature with his existence. The smaller the human footprint, the smaller the consequences for ecology.
Almost all luxurious pleasures, or irrational urges, would have to be left. The capitalist world system of living would have to have been altered to suit the laws of nature.
Birth rates would have to have been organized according to ecological food production. In other words, man would have had to change his anthropocentric culture to a naturalist culture.
The relative truths that individuals seek so much would have to be exchanged for the pursuit of absolute truth, which is linked to the well-being of all beings in nature and their interrelationships.
But man remains anthropocentric, and one cannot even imagine that the world will become naturalist. It should live through the interrelationships of nature's beings, and their improvement. But the goal of the majority is concern for their will.
The rule for nature conservation is to change the human vision, which society is not willing to change.