Nope.

Taxpayers do not need to file a Form 14039, Identity Theft Affidavit, with the IRS regarding an incorrect Form 1099-G. The identity theft affidavit should be filed only if the taxpayer's e-filed return is rejected because a return using the same Social Security number already has been filed.

https://www.irs.gov/newsroom/irs-offers-guidance-to-taxpayers-on-identity-theft-involving-unemployme...