The answer to that is unclear right now.
The IRS will automatically adjust your tax return to exclude the first $10,200 of unemployment compensation and will pay you any extra refund that results from that adjustment. That is supposed to happen starting in May. If that adjustment results in adjustments to other things on your return, the IRS will make those adjustments too. However, if the UEC adjustment makes you eligible for something you did not originally claim, the IRS won't give you that additional tax break, whatever it was. You would have to amend to claim the extra tax break.
The problem is that if you file an amended return now to claim both the unemployment exclusion and any other tax breaks, it won’t get processed until after the IRS makes the automatic UEC adjustment, so by the time your amended return actually does get processed, it won’t be in sync with the tax return that the IRS has on file for you.
My suggestion is to wait for the automatic UEC adjustment and for the IRS to pay any refund due from that. Then, if you are eligible for additional tax breaks, you can file an amended return to claim them. You will have to use as the "base" of the amended return, your tax return after the UEC adjustment and not the tax return you originally filed. Hopefully Turbotax will have a procedure for this once the IRS makes their adjustments.