Thank you all. A helpful range of answers.
c100driver and 172_driver, my question was specific to flying P-RNAV STARs and SIDs with an aircraft that is equipped to fly RNAV/GNSS but is temporarily prohibited from flying DME/DME P-RNAV due to the MEL. In those circumstances, I'm not sure the ANP would reveal anything.
As Skyjob has pointed out, it seems a P-RNAV procedure that (for some reason) still requires DME/DME arcs will state those requirements.
Skyjob, until I started looking in earnest I had not noticed any PRNAV1 SID or STAR plates that mentioned a DME requirement. Many such plates do not even show a VOR or DME for obvious reasons.
However, I flew a TOSVI2U RNAV1 into LROP the other day. Interestingly this plate actually lists the VORs that must be serviceable for P-RNAV DME/DME operations. I have also seen other P-RNAV procedures which simply include the note 'DME'.
In the absence of such notes, I think you're right - good to go.