No, but you can use VBA to set the date in any format you wish:
put this in your ThisWorkbook code module (right-click the workbook
header and choose View Code):
Private Sub Workbook_BeforePrint(Cancel As Boolean)
Dim wsSheet As Worksheet
For Each wsSheet In ActiveWindow.SelectedSheets
wsSheet.PageSetup.LeftHeader = Format(Date, "dd mmmm yyyy")
Next wsSheet
End Sub
Substitute .Centerheader or .RightHeader if desired.