For us if you are flying a conventional non preciccion approach you can allow the FMS to guide the airplane but you must have the raw data displayed to confirm that a valid path is being flown.
In your case the legality would depend on wether the dme arc was flown in IMC or VMC and wether it was above or below the MSA.
What you must ask your self is what would you do if while flying below the MSA you got a "position disagree" type message. RNAV approaches take this into account while a conventinal non precission approach doesn't. For expample it may ask you to get to a dme point before turning on the missed approach. If the DME is not working and your FMS spits the dummy you are left with limited options.