Probably not. You'll have to ask you employer if that's how they plan to handle it. If they intend to reduce your pay until the money is paid back, they may handle it that way. See below for how it is usually handled, tax wise.
Repayments. This situation is described in IRS Publication 525. pgs 34-35. You can take a misc itemized deduction, on line 28 of schedule A (not subject to the 2% of AGI threshold) Or you can take a credit. The credit is computed by refiguring the tax return from the previous year as if the income had not been received. Then the difference in tax is claimed as a credit on the current year's return. In the forms mode (the forms mode is not available in the on-line versions of TurboTax[TT]), you can use the line 73 smart work sheet to enter the credit amount on line 73; select item D, claim of right under IRC 1341 for repayments. TT will enter "I.R.C.1341" on the line next to box d on line 73 of form 1040. TT does not do the calculation or compare it to the alternate deduction.
So, the taxpayer has the option of either claiming the credit or deducting the repayment as a miscellaneous itemized deduction, whichever provides the greater benefit. But, you cannot file an amended prior year return. If the amount is $3,000 or less, only the miscellaneous itemized deduction is allowed and is subject to the 2% of AGI threshold; it goes on line 23 (instead of line 28) of schedule A.