There is no way to know the answer to this question with any certainty. There are arguments to be made for both sides.
On the one hand, it is plausible to say that a zero growth economy could help to solve our environmental problems. From this point of view, growth is made possible by things like greater use of fossil fuels. Growth tends to be defined as greater amounts of consumption. Given these facts, less growth should mean less pressure on the economy. If economic growth stopped, there would not be increases in demand for things like fossil fuels and the environment would not degrade as rapidly.
However, it is also possible to argue that more growth is what we need in order to help the environment. From this point of view, economic growth leads to better technology. Better technology can improve the state of our environment. For example, it is economic growth that allows things like the development of hybrid and/or electric cars that reduce fuel consumption and help the environment.
Thus, it is possible that a zero growth economy will help the environment, but it is not clear that it will do so.