The issue here is complex, as the Social Security Administration (SSA) has traditionally viewed things differently than USCIS. But currently the SSA will issue a SSN to a L-2 visa holder, and I believe that in the state of GA, you need a SSN to obtain a driver's license. You can review information on the SSA's position here:
(Note the ** in the chart, when discussing L-2 visa holders).
However, even though a L-2 visa holder can obtain a SSN without an EAD; in order to work, the EAD is required. At least that is the current position of USCIS. An employer must see an EAD to confirm work authorization for a L-2 visa holder. This was discussed in April 2007 liaison between the American Immigration Lawyers Association (AILA) , the SSA, and the US Dept of Homeland Security (DHS). The relevant meeting minutes are here:
QUESTION: E and L Spouses. Thank you for updating guidance that E and L spouses do not need to present EADs when applying for SSNs.
ANSWER: POMS RM 00203.500 (https://s044a90.ssa.gov/apps10/poms.nsf/lnx/0100203500!opendocument) advises that E-1/E-2 and L spouses may work inherent to status without an EAD upon proof of spousal relationship to the principal. RM 00203.600 is less clear. Will SSA consider clarifying the latter RM?
Answer. SSA has verified that RM 00203.600 has been corrected and clarified. See https://s044a90.ssa.gov/apps10/poms.nsf/lnx/0100203600!opendocument.
QUESTION: We continue to have enumeration problems with L spouses and E principals and spouses. Issuing social security numbers incident to status represents a large number of our liaison requests. Any ideas how to improve getting this important information out to the field offices?
ANSWER: CIS agreed to work on a table/overview of cases likely to go to secondary (EAV) because there are numerous categories that still present difficult, though predictable, verification issues for SSA.
QUESTION: We understand that SSA updated its guidance on E and L spouses based on USCIS guidance that these individuals are authorized to work incident to status. However, there is much confusion about whether an EAD is required for I-9 purposes to work, which we do not believe it should be. We believe the public would benefit from clarification on this issue.
ANSWER: SSA and CIS both agree that the spouses of Es and Ls are authorized to be employed incident to status. However, CIS believes that an EAD is required for I-9 purposes under the regulations. CIS has agreed to consider this issue, and the Committee has again presented authority for the proposition that E and L spouses, like asylees, are authorized to work incident to status and do not require an EAD for I-9 purposes.
So to clarify, a L-2 visa holder can obtain a SSN without an EAD; but to work, the L-2 visa holder needs an EAD. Crazy, I know.