No is the answer. ADF cannot be mandatory for IFR as it is not now mandated for carriage in those conditions.
Officially you are of course restricted to Approaches and Holds not requiring an ADF.
In the real IFR world for ADF procedures, you would select the radio aid from your GPS database, and use the OBS facility to select and fly the inbound Course of the Hold or Letdown on your CDI or map display. . Much easier and of course safer than the wandering ADF needle.
Re DME the slant range errors vs GPS are negligible during an approach,as the FAA have long mandated, and thousands of FAA IR pilots accept and safely use daily.