What you are saying does not make any sense. You cannot fly a 'GPS Coupled Approach' on an ILS, you would have to couple the AP to the localizer/glide slope to fly a coupled ILS. Otherwise you will just follow the localizer course in the GPS database. You are not supposed to do this. The ILS approaches in the GPS database are for sitauational awareness only. You are not even supposed to fly a localizer approach this way, even though it would be possible to do so.
To fly a coupled approach with an autopilot you should tune and ID the localizer and couple the autopilot to that. To get DME info you have two choices. In the GPS you can either pick the navaid that is depicted on the approach plate for DME, or load the ILS approach from the GPS database. If you pick the approach from the GPS database it will give distance to the fixes listed on the plate, then cycle to the next fix. For instance if you are on the localizer the GPS will show how far you are from the outermarker, then the mm, then the runway threshold. If you pick the navaid that is used on the plate you would pick the VOR or the localizer, etc. Then you will have DME just as it is depicted.
When I am flying an ILS approach I prefer to use the navaid depicted on the plate. It is less confusing and it is easier to just put in 'Direct' to the navaid than load an approach. This also has the advantage of not having the GPS go into suspend mode after you go missed like it does after you cross the runway threshold if you actually loaded the approach.