A while later I realized that we had just done a DME Arc with no DME! Which led me to a discussion with another captain; our reliance and expectation of our FMS is such these days that we forget that except for RNAV approaches all other NPA are not meant to be flown by the FMS alone. So long as the chart says, VOR, DME, or NDB the said ground aid should be fully serviceable, even if we are going to let the box manage. Technically and legally speaking that is. I think.
Going by my manuals, an overlay approach is a specific technique to aid approach navigation when the the specific procedure being flown is NOT in the FMC database. The overlay technique permits the use of an alternative approach that matches the course and profile. For example, loading up an ILS approach that has the same flight path as the VOR/DME procedure when the VOR/DME approach is not available in the FMC. When using an overlay approach, the actual
raw data is the primary reference and must be servicable.
However, for non-ILS work and transitions, when loading up the specific VOR/DME approach in the FMC to fly an the appropriate VOR/DME procedure raw data is not required (but is recommended) unless unless following a localiser. The FMC is the primary means of navigation. So it would have been legal for me to fly the approach with the DME unservicable.
Just take the Boeing ILS approach procedure for a ILS VOR DME approach. The normal Approach Procedure and the FMS expects you to have the ILS tuned at the IAF, even if you are flying a procedure transition based on a VOR/DME (arc, racetrack, base turn, etc). The Boeing FMC is intended to be used as the primary means of navigation when the required procedure is contained in the database.