An overlay should say, for example, VOR/GPS RWY 27 etc. in my present jet's FMS's it would be shown as VOR27G (with the added benefit of a VPATH), don't know about the G1000 system - it's been a long time since I flew a DA42, my only Garmin type. Even so, if available, I don't see why you wouldn't use all the 'tools of the trade' and load that approach on the G1000 and back it up with the raw data needles. Why dive & drive?
I don't even think that the FAA regs still require the navaid to be tuned anymore... That's just down to airmanship I guess. EASA still does require this
AFAIK.
I believe you could use LNAV for conventional approaches as long as raw data is monitored.