No, a Form 1099-G Certain Government Payments requires TurboTax Deluxe edition or higher.
Unless... you qualify for the Free File program. https://ttlc.intuit.com/replies/3301359
Even if state and federal taxes were with held from my UNEMPLOYMENT
You cannot use the Free Edition of TurboTax. Form 1099-G is not supported in the Free Edition. Our Deluxe version would work well for you, though.