Yes… when we talk about hunting promoting conservation, the ecological harm caused by deer overpopulation is something to keep in mind. From a hunting perspective, that’s still a positive outcome. From other perspectives, it isn’t.
Overpopulation of deer, though, is in part an ecological impact of hunting—through killing predators* and managing land specifically to favor high deer populations**. So hunters are at both ends of the process—helping to reduce an overpopulation problem that they helped to create.
* Promoting hunting certainly isn’t the only reason people kill predators, but it historically has been, and in parts of the western U.S. continues to be, one of the reasons.
** Though generally forgotten now, rebounding of white-tailed deer from a steep decline was one of the big early success stories of conservation in the U.S. Promoting huntable animals continues to be a focus of public land management—sometimes with net ecological benefits, sometimes the opposite.