This is untrue. Adam cannot do good without God.That really doesn’t quite work. God clearly created Adam with the ability for good and bad, but as the myth goes, with freewill to choose between them.
His created nature did not include both good and bad, for God looked at his creation and said it was "good." Adam's nature was good, and Adam's free will was good, but this free will allowed Adam to disobey God. Yet when someone is filled with grace, he does not have to draw upon the Law to act properly but does so by nature. Hence Paul says that he is no longer under the law but above.So no Adam didn’t go against his created nature since his created nature included both good and bad.
Besides being filled with original grace, Adam was created in a state of trusting God; he would otherwise not be good nor have grace. Adam broke this trust by disobeying God, by believing what the serpent said.
Overall, I think you are over-analyzing what the text says. If Adam had no knowledge of what obedience was, we may as well say that Adam had no knowledge of knowledge. For to have any knowledge at all, one must trust the source of the knowledge, though we aren't always conciously aware of this.