The main economic issue here is the existence of externalities. Externalties are when there is flow on effects to parties outside the buyer and producer (3rd parties). There can be positive externalities, such as education and flu shots; and also negative externailties, damage to the environment being a clear example. When there is existence of externalites is means there is market failure within the economy or the particular industry, and government intervention is required to account for these externalties.
When there is simple production of a good or service, there is a simple supply and demand graph to indicate the equalibrium price and quantity. This shows the marginal cost (being supply) and the marginal benefit (being demand) meeting together. However, when there is existence of negative externalities ie. enviroment impacts, the marginal cost does not include the full costs of the good or service. Thus to factor in the total costs (marignal costs plus social costs) the supple curve should shift to the left which should result is a higher price and decreased quatity. This would produce the equalibrium for society.
(it would be easier to explain with a graph, but i think you get the idea)
I don't believe that there would be direct benefits for the environment from economic growth. However, you could argue that when there is increased economic growth there is increased taxation revenue for the government which can be used for government spending towards environment protection.
You can also look at the two main forms of government intervention with the market failure of negative externalties; which are taxation and tradeable permits.