No, you cannot.
Unfortunately, altering the CustomUI file won't let you hide it. VBA must be used to hide the formula bar. You may just do the hide operation on the Workbook open event after all.
Private Sub Workbook_Open()
Application.DisplayFormulaBar = False
End Sub
You can turn it on/off depending on the active sheet like so:
Private Sub Workbook_SheetActivate(ByVal Sh As Object)
If Sh.Name = "Sheet1" Then
Application.DisplayFormulaBar = False
Else
Application.DisplayFormulaBar = True
End If
End Sub