Airmann,
If the traditional NAVAID is down for the approach, what data is your FMS using to continue providing guidance to you?
The FMS has multiple inputs including INS, GPS, WAAS, VOR, NDB, etc. It processes all inputs through a Kalman filter to provide one position solution. It uses this to plot your position relative to the FMS database points. That's the basics of an FMS.
So when you lose your traditional (VOR or NDB) then your FMS continues to provide a position solution to you using the other inputs from the system. However, if you are required to use the VOR or NDB for "final approach course guidance" then you must discontinue the approach - regardless of how accurate your position solution from the FMS currently is.
Now, with regard to your original question, I don't believe you did anything illegal or unsafe - provided the FMS was giving a position solution for the loaded DME arc without any warnings, and you used the ILS once you intercepted to fly to the runway.
The ILS RWY 08 approach into CYBR I think is a good example of the approach that you are asking about.
http://imageserver.fltplan.com/merge...ILS_RWY_08.pdf
The title of "ILS RWY 08" indicates that you only require the ILS to fly the final approach course. Prior to the final approach course you may use another means of navigation (provided it's set up correctly and you adhere to the limitations for that navigation source [FMS]) to fly the procedure. In this case, I could fly FMS direct to LISTU and then start the DMC arc as programmed by the FMS all the way to the final approach course, at which time I'd intercept and fly the ILS. Or I could go FMS direct to KESVA for the straight-in ILS if I was coming from the west. Prior to flying the 085 degree course inside of KESVA, you may use another nav source to navigate... which seems quite obvious in this case since the ILS only works when lined up on the final approach course!