Hi! I'm a TurboTax Live CPA. You can but it most likely will not result in them processing an unemployment adjustment any faster. Prior to making contact with the IRS make sure that you are due a refund from the additional exemption. Did you have any tax (line 16 on your 1040) on your original return. If you did not, it is very unlikely you will be receiving an additional refund since you did not pay tax on the unemployment originally. Certain non-refundable credits can also negate the effect of the unemployment exemption.
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