Yep, woody species would eventually take hold with sweetgum being one of the first ones to arrive on the scene......but it would go through a progression to get to that point. It would start out with your pioneer understory plants and then transition to the ones that are more favorable to wildlife.....things like pokewwed, ragweed, dewberry, etc.....It's the change in soil conditions that triggers the more favorable plants to germinate and grow. It's also the change to a more fungally dominated soil that brings on the woody species. The key to good fertile vegetative growth is to continue to allow the soil to progress but reset the succession of the vegetation without destroying the soil in the process and reverting it back to the pioneer plants