My prediction is that IRS will eventually refund the $600 without further action required -- but they will subtract any ES penalty, and other penalties and interest if this payment was made after the due date.  And you have to hope that the taxpayer doesn't owe other taxes for other years.  

It won't happen until the return is processed, so if there is a delay because of issues like RRC or identity theft, don't expect the check for a few months.  Or maybe many months.  Keep IRS advised of any address changes.