Yes, once your 2020 tax return is processed, the IRS will review and reconcile any missing third round stimulus payments. These plus up payments will be sent separately from your tax refund.
Here is a link for reference.
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So if I received a check for plus up for the 2020 additions on my taxes does that mean my 2020 taxes have been approved. I only ask because the tool still shows pending.
The IRS tool should say PROCESSING and it may never say approved since the tool has always been buggy. The fact you got a PLUS UP payment is a good sign things are moving along so check the IRS site every few days but don't be surprised if the system never gets updated.