No, you are correct, you can't report your 1099-R in your Federal Return to claim State Tax Paid with $0 in Box 1.
Unless you are filing Itemized Deductions, you wouldn't get a deduction for them anyway.
However, you should be able to claim State Tax Paid on your Georgia State Return.
You may need to add them under 'Other Deductions' or some similar heading as you go through your State Return Interview.
I hope you have notified your Payor to stop withholding these taxes going forward.
Click this link for more info that may help you with Georgia Military Benefits.
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