If your asking whether unfettered, laissez-faire, deregulatory capitalism is the answer to solving the ecological crises we currently face, the answer is ... um ... no. In case you didn't notice, most people who take this stance deny that these crises exist in the first place, or at least believe these crises aren't very serious.
That said, this statement is a little misleading.
Increases in growth also implies the exhaustion of resources at similar rates.
Economic growth can occur without a proportional impact upon the environment, by using our resources more efficiently by improving technologies and resource management.
Economists tend to pretend that we do not live in a biosphere, that we can grow forever...
These people are bad economists. Natural resources, like all other resources, are assets which can and should be assigned a value. Good economists attempt to do this, through the process of full-cost accounting. Passing the societal cost of destroying or damaging this asset on to the consumer is the responsibility of the government, which can do so through pollution taxes or fines.