While Georgia does have tax legislation on the books to encourage high-deductible health plans (HDHPs), it would not have an impact on your tax return.
You can include HDHP premiums as an adjustment to your Georgia income only to the extent it wasn't already deducted from your Federal adjusted gross income (or if you itemized deductions, the amount eligible to be claimed could cause an additional adjustment). If your premiums were paid pre-tax, these amounts have already received a tax benefit and are being excluded from your Federal income.
Since the state return pulls in your Federal income, you cannot deduct these premiums again since they are already excluded. Therefore, yes, the premiums are still not taxed on your Georgia return, but there is not an additional deduction.
If the premiums were paid privately with your after-tax dollars from your paycheck - those premiums would be eligible for a Georgia deduction. That does not sound like the case though.
For further information, please refer to Page 16 of the Georgia IT-511 instructions at the link below.
https://dor.georgia.gov/documents/2015-it-511-individual-income-tax-booklet
