I don't think so, since nature can't be assigned a value. That's why we've been destroying nature, because in capitalist terms it only gains value once we use it to do something. A tree in the Amazon : no value. The same tree once it's cut off : value, because you can now sell it.
Also, capitalism deals with short-term, while any serious green philosophy can only be considered on the long term.
So capitalism can become greener obviously, but it won't be a green economy either. And the fact that they sell green/bio products here and there and plant a tree for every cup of coffee you drink won't change that, as long as you don't change the fondamentals of capitalism which is that the environment has no value. Not in the sense that it has no value, but in the sense that capitalism has no tools to properly access the value to our well-being of clean air, clean water, healthy food, trees, etc. Hell, capitalism is not destined to increase well-being anyway, but wealth.