This was covered about a year and a half ago. A search would have had trouble finding it because of all the dashes in the title:
ILS vs. ILS or LOC approaches....???
It seems that most civilians don't do it, but it is perfectly legal to fly a localizer if you are cleared to "Fly the ILS..." Military pilots do it daily. Over and over again, ad nauseum. However, not the other way around. If you are cleared the "Localizer approach..." you cannot fly the ILS because the gs is not part of the localizer approach.