Not really. After all, why say "elm" or "birch" or "oak" instead of "tree", since that's all they really are? Because the elm is graceful, slender, swaying in the wind, the birch is brilliant white against a backdrop of brown, and the oak is sturdy and stalwart. Three entirely different types of trees, with three entirely different connotations.

Emerald is a particular shade of green, notable for the brightness and clarity. This is distinct from moss green, hazel, or blue-green. To reduce all of them to "green" renders the color generic and devoid of subtlety and meaning.