It’s not a requirement to enter your driver’s license to file the return (unless in Alabama or Illinois, since they require it), but it could possibly delay it being processed in some states if you do not enter it. Most states will make note of the drivers license delay on their refund tracking page. If you don't see a note there, it may not be a big deal for your state.
Some states may request your driver’s license number for state tax returns because they have the ability to match state records and help confirm your identity. Please see below for more details.
Per Georgia's Department of Revenue:
Georgia has stated to please allow them 90 business days to process your return and issue a refund. This is also stated on their Where's My Refund? page when you go to track your refund. If you are not finding your return in the system, this is why, they may have not started processing yours yet. It will not show in their system until they actually start processing it.
Why are you asking for my driver’s license or state ID?