Bookworm.
Legislation requires you to carry navaids appropriate to the type of approach to be flown which would seem to imply, given that GPS overlay approaches are not yet approved in our airspace, that you need to carry an ADF. Further to that even where they are approved, ie US, you are still required to have the appropriate navaids aswell as your GPS.
Given that most ILS approaches in this country use an NDB as the IAF it also seems reasonable that you need to carry an ADF to legally fly an ILS unless of course radar unserviceability is something which will never happen to you.
Also before trust your life to a GPS, the "No GPS position available" message is something which I have seen more than once.