I'm in Acworth, GA just about 10-15 miles from you and have not had any issues with cops. I use a Bicycle helmet when I ride. You can get a 1/2 face DOT moped/scooter helmet pretty cheap off eBay and they are not that big. To my knowledge of the Georgia law which I try to abide by, you need to be below 50cc and the bike has to have pedals. The written law is pretty basic and doesn't address motorized bicycles specifically but rather they are considered Mopeds. A standard drivers license is needed and when on main roads you should have lights and follow all road laws just as a bicycle would. I don't have turn signals so I use my arm and use the proper signals.
In general if you don't act like a crazy person zooming in and out of cars and try to adhere to the standard rules of the road you should be ok.
We go routinely go by the Big Chicken on the way to Krispy Kreme to take the kids. Maybe we will see you cruising sometime.
Enjoy the ride!