It looks like this would not work, as documented in the IRS' Offset instructions (bold mine):
Internal Revenue Code IRC (§) 6402(a), (c), (d), (e) and (f) require a taxpayer's overpayment to be applied to any outstanding Federal tax debt, child support, Treasury Offset Program (TOP) debt, State income tax obligation or Unemployment Compensation prior to crediting the overpayment to a future tax or issuing a refund.
However, there is a method for applying for an exemption. From IRS Publication 4012, the volunteer resource guide:
If a taxpayer would face a hardship from a tax refund offset
and has only outstanding Federal tax debts, he or she can
request an Offset Bypass Refund (OBR) from the IRS.
Refer the taxpayer to the Taxpayer Advocate Service to
see if they meet TAS case acceptance criteria. The OBR
typically should be requested before the return is filed
because the OBR must be approved before the refund is
The OBR is documented here.