Probably not. Main highways in Georgia tend to have narrow shoulders full of rumble strips. It will really drive you nuts. If you go that way you would most likely do better sticking to back roads.
I would recommend taking US90 to Jacksonville and heading north on US17 (good shoulder, no rumble strips) but I don't know how you would skirt around Jacksonville. Taking 301 and A1A from Baldwin to Yulee is out of the question. That stretch is really bad - narrow two lane, shoulderless and heavily trafficked although they are improving it in places. You could try 121 up to Folkston but I don't know anything about it. Or pick your way through Jacksonville.
If you go up US17 you can skirt around Savannah by taking Dean Forest Road (307) to Port Wentworth and crossing the river on the old bridge.
US17 through Georgia and between Hardeeville and Walterboro in South Carolina is good bicycling road. The interstate takes all the traffic.
Do NOT approach Charleston by taking 17 or 17A between the Interstate and Charleston or Summerville. They are very bad stretches of road. Go up to 61 and ride it into Charleston. It is not ideal but is much, much better. You can get from Walterboro to 61 by going east on 17A a few miles to Sidney's Road and up it to 61. This is the ACA route.
Richmond Hill and Hardeeville have very cheap, clean motels. They compete fiercely. I like the Motel 6 in Richmond Hill which also has a KOA.