If all people understood the common heritage that we have with the Earth and our environment - namely, that the very atoms that make up our bodies were formed in stars, just like the atoms in rocks, in the atmosphere and in every living thing - would people be more inclined to treat the environment with more care?

No

Explanation:

It is one of those harsh realities that no matter how hard we try to connect people to their roots aka make them understand that everything is interconnected like the breathe you throw out is used by plants in photosynthesis, the O2 plants give is used by us. Living beings and Non-living beings are all connected and most humans know about this. But, when it comes time for earning the $$$, people's judgements are often clouded by their greed hence no matter how hard we try to make people understand we are all connected and that they should take care of the environment more, they will likely treat the environment as they always have been: to serve their financial and selfish needs.

TLDR: People are selfish hence probably will not treat environment with more care even if we educate them about our interconnectedness.