Probably not. As long as the omission in box 10 did not lead you to take the dependent care credit too. If you used the pre-tax contribution made in FSA account to pay for your childcare expenses, you cannot take the Dependent Care Credit.
As the child care funding in your Flexible Spending Account FSA is considered as a pre-tax dollar contribution, you can take the Dependent Care Credit ONLY on the expenses paid exceeding the total amount contributed in the FSA. For example, if you are allowed to put in $5200 in your FSA as a pre-tax contribution , you are not allowed to take the credit unless you spent more than $5200 on the child care expenses.
Just to be sure, you can do a mock return using the corrected W-2 when you get it and see if it changes anything. If it does, do the amendment, if not then you don't need to worry about it.
FSAs are usually funded through voluntary salary reduction agreements with your employer. No employment or federal income taxes are deducted from your contribution. The employer may also contribute.
Note: Unlike HSAs or Archer MSAs which must be reported on your Form 1040, there are no reporting requirements for FSAs on your income tax return.