No, since the repayment was made in 2019, you must report the payment either as a special itemized deduction not subject to the 2% rule, or as an IRC 1341 credit, on your 2019 return. The adjustment to the W-2 only corrected your social security and medicare tax (and hopefully your employer refunded the difference or applied it as a credit to the repayment). To recover your state and federal income tax, you report the repayment on your 2019 return.
