I don't think so. Dove aren't included on Harvest report, just resident game birds and I didn't see them on the list. They are on the Federal HIP survey and that is just for migratory species. I might be wrong, but I think they are regarded the same as pigeons.
You don't say whereabouts you are, but they are everywhere. Literally. Learn what they look like and you will see them. They tend to act more like pigeons than mourning doves. They seem to like hanging around structures which can be problematic since you have to be 150 yards away from inhabited structures. But find a good spot and the take can be large. Just don't shoot more than you are willing to clean and eat.