This doesn't quite do justice to the idea that, spiritually, we are "cursed," "blind," "dead," "children of wrath," and ultimately "enemies." It would mean there is no friendship with the enemy which would require a "putting" of enmity between her offspring and the serpent's. 

The only problem with the idea of "cooperating with grace" is that enemies...not only do not cooperate, they actively resist. (Which seems to be the point of the end of Romans 1.)