It will absolutely affect the IRS records and the amounts they have on file for your withholdings.

When you correct the mistake - make sure Paychex sends in an amended W2 to the IRS for you for 2019.

Timing may be an issue - but you should file your taxes on time and with the W2 information they provided. You may get a letter from IRS with the discrepancy in withholding amounts but will just need to call them and work through it, but hopefully, the Paychex amended information gets in quickly to the IRS system.