No it does not. In fact, your actual W-2 does not show a filing status. Some employers have an information section on the side of a W-2 form showing the filing status that you used on your W-4 to indicate how much tax you wanted withheld, but that is not reported to the IRS, nor does it dictate what to put on your tax return.
Use the correct filing status for your situation--Single, married filing jontly, married filing separately, Head of Household or Qualifying Widow(er)