Cars can't pass on the shoulder, neither can bikes. .
According to the interpretation presented in the Georgia Bicycle Law Enforcement Pocket Guide, they can:
When Overtaking and Passing on the Right is Permitted [§40-6-43]
The driver of a vehicle may overtake and pass upon the right of another vehicle only under the following conditions:
• When the vehicle overtaken is making or about to make a left turn; or
• Upon a street or highway with unobstructed pavement of sufficient width for two or more lanes of moving vehicles in the direction being traveled by the overtaking vehicle [§40-6-43(a)(1,2)].
If otherwise authorized, the driver of a vehicle may overtake and pass another vehicle upon the right only under conditions permitting such movement in safety. Such movement shall not be made by driving off the roadway [§40-6-43 (b)].
(A cyclist traveling in a bicycle lane, or in a lane wide enough for motor vehicles and bicycles to share (see roadway position above) may pass motor vehicles on the right, but must still take care to avoid turning vehicles. This is allowed since in these cases there is either provision of a lane or sufficient width for two lines of moving traffic; one of which is bicycle traffic.)
I'm not sure of the exact status of this document, or the organisation producing it, but it seems a reasonable interpretation to me. There's a bit about it about half-way down on the front page of the site.