No, environmental cases should not be tried in International Criminal Court, because that gives the nation's power to another government. Citizens of the United States are not subject to international law. They do not know that they have broken a law, and it would martial law to turn them over to the punishment of another court of law.
A court that can focus on environmental cases should be made so that environmental cases are addressed properly. ICC on the other hand, is already prosecuting individuals for genocide, crimes against humanity, and war crimes . Clearly with the jurisdiction of ICC, it should not include anymore environmental cases so that it can concentrate on its current range of powers.